On the Feynman Rules of Massive Gauge Theory in Physical Gauges

Understand

For a massive gauge theory with Higgs mechanism in a physical gauge, the longitudinal polarization of gauge bosons can be naturally identified as mixture of the goldstone component and a remnant gauge component that vanishes at the limit of zero mass, making the goldstone equivalence manifest.

• In light of this observation, we re-examine the Feynman rules of massive gauge theory by treating gauge fields and their corresponding goldstone fields as single objects, writing them uniformly as 5-component "vector" fields.
• The gauge group is taken to be $SU(2)_L$ to preserve custodial symmetry.
• We find the derivation of gauge-goldstone propagators becomes rather trivial by noticing there is a remarkable parallel between massless gauge theory and massive gauge theory in this notation.