Based on example 10.3 in the textbook, the Proca Lagrangian for a vector (spin-1) field is written as
L=-(1)/(16\pi )F_(\mu ) u F^(\mu v)+(1)/(8\pi )((mc)/(?))^(2)A^(v)A_(v)
where the field strength tensor is defined as
F_(\mu ) u =del_(\mu )A_() u -del_() u A_(\mu )
, and
m
is the mass of the vector field. Applying the Euler-Lagrange equation of motion, derive the field equation
del_(\mu )F^(\mu v)+((mc)/(?))^(2)A^(v)=0.
Why does the Proca Lagrangian not preserve gauge invariance? Can you explain why the photon is a massless particle?

Question

Based on example 10.3 in the textbook, the Proca Lagrangian for a vector (spin-1) field is written as

L=-(1)/(16\pi )F_(\mu )
u F^(\mu v)+(1)/(8\pi )((mc)/(?))^(2)A^(v)A_(v)

where the field strength tensor is defined as

F_(\mu )
u =del_(\mu )A_()
u -del_()
u A_(\mu )

, and

m

is the mass of the vector field. Applying the Euler-Lagrange equation of motion, derive the field equation

del_(\mu )F^(\mu v)+((mc)/(?))^(2)A^(v)=0.

Why does the Proca Lagrangian not preserve gauge invariance? Can you explain why the photon is a massless particle?

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