Maxwell Equations in Potential Fields

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Question:Maxwell Equations in Potential Fields

Posted: Inacio Aprendanet 65 Product: Maple

May 02 2017

I wish to express the Maxwell equations in potential fields deriving from a Lagrangian in cartesian coordinates, but expressed in vectorial form; But I am receiving an message error that I do not understand.

Field_A-MaplePrimes.mw

Initial Definitions:

I wish in this work to express the Maxwell equations deriving from the Lagrangian in the fields and

(1.1)

but expressed in vectorial form;

(1.2)

$`Detected \`t\`, the time variable, in position 1. Changing the signature of the spacetime metric accordingly, to: + - - - `$

$`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}$

(1.3)

$`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}$

(1.4)

Some definitions

Defining the Maxwell tensor

(2.1)

Defining the field A with their components:

A[mu] = Vector[column](%id = 18446744074366759750)

${F, A[mu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$