Question

Conservative vector fields in Minkowski Space?

Answer 1

A conservative vector field (also called a path-independent vector field) is avector field whose line integral ∫ C F ⋅ d s over any curve depends only on the endpoints of . The integral is independent of the path that takes going from its starting point to its ending point.

Answer 2

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✔️✔️I wasn't sure if the fact that the space and time components in the four/Minkowski gradient had opposite signs meant that some theorems about potential functions and line integrals wouldn't apply.

Also, I was wondering if curly electric and magnetic fields, made curly as a result of time varying magnetic or electric fields, could be expressed as the four gradient of a (possibly complex?) scaler potential.

A conservative vector field (also called a path-independent vector field) is a vector field whose line integral ∫ C F ⋅ d s over any curve depends only on the endpoints of .

The integral is independent of the path that takes going from its starting point to its ending point.


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