Research Notes II, 1949

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Part II

Electromagnetic field with given sources

Charge density Current density satisfy the

eqn of continuity:

Put

Then

Introduce the skew symmetric tensor The Maxwell's equations: μνλ all different (I)

Then f_μν can be expressed in terms of a 4-potential

(II) zero net mass

A generalized equation with rest mass given by μ

[Schweizer?]-Tomonago covariant

In the scalar theory there is no difference whether μ=0 or ≠0. However with vector theory, [?] is quite different for the following reason.

Ψ_μ are not all independent fields. This equation helps to eliminate one of Ψ_μ. If μ=0, under the gauge transf^[n?]

gauge-invariant quantities

The scalar & vector potentials are not physically observed qualities. Only the field strengths are observed, significant because the force is determined by them. (For μ≠0, the gauge invariante does not hold.) It is customary way to choose the right gauge at which . (which is not in general true). Gauge transfⁿ [?] can be made.

Suppose μ=0

In the gauge

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