Есть ли официальное название «пары Лоренца», как энергия и импульс?

Тензор в точке P является многолинейным отображением, которое берет много со-векторов и векторов и выплескивает скаляр. Векторы / со-векторы также являются тензорами. Компоненты и основа тензоров зависят от координированных систем, но сами тензоры связаны с точками и остаются неизменными независимо от координированных изменений (изменений в системах отсчета).

Мы формируем тензорные поля (векторные / ко-векторные поля также являются тензорными полями), присваивая каждой точке тензор. Используя координаты точки, мы можем затем описать компоненты тензора как функции координат. Скаляр, связанный с P, остается неизменным. В принципе, общий тензор можно записать как ......

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{P} = T_{c . . . . d}^{a . . . b} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}} \otimes \dots \otimes \frac{\partial}{\partial x^{b}} \otimes d x^{c} \dots \otimes d x^{d}

T_{п} знак равно T_{с,,,, d}^{,,, б} ({Икс}_{п}^{1},,,,, {Икс}_{п}^{N}) \frac{\partial}{\partial {Икс}^{}} \otimes \dots \otimes \frac{\partial}{\partial {Икс}^{б}} \otimes d {Икс}^{с} \dots \otimes d {Икс}^{d}

Не думайте о дифференциалах и частных производных символах в их обычном смысле, здесь они обозначают базисные векторы / со-векторы. Из этого удобного представления мы можем восстановить свой обычный смысл. «Гравитация» Торна, Мизнера и Уилера объясняет, как мы можем это восстановить.

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{P} = v^{a} (x_{P}^{1}, . . ., x_{P}^{n}) \frac{\partial}{\partial x^{a}}

v_{п} знак равно v^{} ({Икс}_{п}^{1},,,,, {Икс}_{п}^{N}) \frac{\partial}{\partial {Икс}^{}}

И двойной вектор (со-вектор) обозначается через

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

w_{P} = w_{c} (x_{P}^{1}, . . ., x_{P}^{n}) d x^{c}

{вес}_{п} знак равно {вес}_{с} ({Икс}_{п}^{1},,,,, {Икс}_{п}^{N}) d {Икс}^{с}

Но как тензор выплескивает скаляр? Ну, это происходит через карту при P

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d x^{a} * \frac{\partial}{\partial x^{b}} = δ_{b}^{a}

d {Икс}^{} * \frac{\partial}{\partial {Икс}^{б}} знак равно δ_{б}^{}

Так что задан тензор типа

(n, m)

(n, m)

(N, м)

$(n,m)$ при P,

n

n

N

$n$ со-векторов при Р и

m

m

м

$m$ векторов в P, мы получаем скаляр в P (используя приведенное выше отображение)

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{P} (v_{1_{P}}, . . . ., v_{m_{P}}, w_{1_{P}}, . . . ., w_{n_{P}}) = T_{c . . . . d}^{a . . . b} v_{1}^{c} . . . v_{m}^{d} w_{1 a} . . . w_{n b} = f (x_{P}^{1}, . . ., x_{P}^{n})

T_{п} (v_{1_{п}},,,,,, v_{м_{п}}, {вес}_{1_{п}},,,,,, {вес}_{N_{п}}) знак равно T_{с,,,, d}^{,,, б} v_{1}^{с},,, v_{м}^{d} {вес}_{1},,, {вес}_{N б} знак равно е ({Икс}_{п}^{1},,,,, {Икс}_{п}^{N})

Любые введенные 2 вектора / со-векторы могут быть равны. Изменение координаты может изменить компоненты. но сумма их продуктов остается неизменной при P. 'Gravitation' от MTW, которая явно демонстрирует эту координирующую независимость.

Есть ли официальное название «пары Лоренца», как энергия и импульс?

Ответы

qsugon

dj_mummy