The free-field Lagrangian density, with = h /mc, was introduced by Alexandre Proca in 1936

The free-field Lagrangian density,

with = ℓ −h/mc, was introduced by Alexandre Proca in 1936 as an alternative to Dirac’s theory of the positron. Today, it serves as a model for electrodynamics with a photon with mass m when matter-field coupling is added to get the total Lagrangian density,

(a) Find the effect of the Proca mass term on the Maxwell equations.
(b) Show that the Proca model violates gauge invariance because a particular choice of gauge must be made to guarantee conservation of charge.
(c) Find the scalar potential for a static point charge q in the Proca model.

Transcribed Image Text:

ƏA 1 LP = { ₁0 [(√x + 3 A) ² - 2²0 × A³²] - 2² [A² – (w/c3ª], (V - Ət 2μol²