Effective Lagrangian in spontaneously broken gauge theories

Abstract

In gauge theories of weak and electromagnetic interactions, it is generally assumed that the addition of extra groups [simple or U(1)] commuting with the standard Weinberg–Salam SU(2) -U(1) group, generates new degrees of freedom for the model, simply because there are new coupling constants in the game. This assertion is not true in general. When looking at the effective Lagrangian of the physical system (−q2 much smaller than any mass of the massive vector bosons), we see that a coupling constant completely disappears if the generators of its corresponding group do not enter in any surviving unbroken subgroup [U(1) for Weinberg–Salam model]. In those cases, the novelties are provided only by the quantum numbers of the fields and especially by the arbitrariness on the choice of ’’unphysical’’ Higgs fields. This effective Lagrangian is defined and constructed in the case where the initial and final symmetry groups are direct products of simple groups and U(1) groups. Some of its remarkable properties are investigated.