Weak and Electromagnetic Interactions in Superconductivity Model

Abstract

Starting with a Lagrangian of self-interacting lepton fields only, we construct an effective Lagrangian of the W einberg-Salam type. This shows that the photon, the Higgs boson and the weak-vector bosons are all composites of lepton and antilepton. Arbitrary parameters involved in the original WS model are largely removed. W einberg 11 and Salam 21 (WS) have proposed a unified model of weak and electromagnetic interactions through the use of the Higgs mechanism. In their model there are many elementary fields, i.e., the Riggs-scalar boson, the weak­ vector bosons, the electromagnetic field, and the leptons. We propose here a composite model of those particles except for leptons. We start with a Nambu­ J ona-Lasinio type Lagrangian 31 which describes a system of self-interacting lepton fields only, and obtain an effective Lagrangian of the WS type. This shows that the created Higgs boson, electromagnetic field, and weak-vector bosons can be considered composites of lepton and antilepton. At this point our program resembles works of Bjorken 41 and others 5> in spinor electrodynamics where they claim that a photon is a Nambu-Goldstone composite boson associated with a spontaneous breakdown of Lorentz invariance. Our pro­ gram is also analogous to the work of Eguchi and Sugawara 6> and its non-Abelian generalizationn where the authors have derived effective Lagrangians for expecta­ tion values of fermion fields which describe interactions among fermion-antifermion bound states in superconductivity models of hadrons. In these works there are certain difficulties associated with the Poincare invariance of the theory. Recently, however, we showed 8l that these difficulties can be avoided if operator equations for fermion fields are adopted, rather than the use of expectation values of fermion fields. Subsequently, Kikkawa 9 l and Kugo 101 proposed a simple derivation of the above effective Lagrangian by making use of the path-integral technique with a trick clue to Gross and Neveu.w In the present paper ~we consider how to realize the WS model in the frame­ work of superconductivity model by using the path-integral technique, and find that arbitrary parameters involved in the original WS model are largely removed. We begin with the following Lagrangian of the WS massless leptons only: