Perturbative gauge invariance: electroweak theory II

Abstract

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.

Quantum gauge models without (classical) Higgs mechanism

“…A developed formulation was found in the treatment of massless Yang-Mills theories [36,37]. It has been applied successfully also to massive non-Abelian models, namely the SM [41,42], spin-2 gauge fields and supersymmetry. Quite recently, the method has been recruited to examine the issue of the (putative) decoupling of ghosts in a class of noncovariant gauges [52].…”

“…The book by Scharf [35], crowning a successful line of research [36][37][38][39][40][41][42][43] which in particular establishes a consistent formulation of the SM without SSB [41], aimed to bring a fresh perspective to the subject from the standpoint of CGI. In tune with it, with the earlier reality check, and with the phenomenological SM Lagrangian, here we stop pretending we know the origin of mass, and start without preconditions again from MVB as fundamental fields.…”

“…CGI for third-order tree diagrams yields conditions restricting h 7 and f 11 (via conditions on h 6 ), which in the case z = 1 determine these parameters uniquely; see the next subsection. The procedure was explained in [42,Sect. 5], with calculations given in detail for the SM; consult [35] as well.…”

“…by inserting the explicit expressions in (39) for I 0 and (41) for L 0 into (42). As explained in [45], the last two terms do not contribute to the nilpotent charge Q in -which is defined only for on-shell fields.…”

Using Painleve Test on the Kinetic System for Yang-Mills Theory

“…Yang-Mills gauge theory with gauge group SU(3)×SU(2)×U(1). Here the first factor is the gauge group of QCD while (SU(2)×U(1)) gauge field is that transmitting what is called the electroweak force [4].…”