Space-time approach to spontaneous symmetry breaking in the Abelian-gauge interaction

TL;DR

This paper presents a space-time framework for spontaneous symmetry breaking in Abelian gauge theories, proposing a new interpretation of the Higgs mechanism through relativistic many-body states and vacuum condensation.

Contribution

It introduces a novel space-time approach to spontaneous symmetry breaking, avoiding the traditional Higgs Lagrangian and analyzing gauge boson condensation and Higgs-like boson emergence.

Findings

Vacuum condensation of fermion-antifermion pairs and gauge bosons occurs.

A Higgs-like boson emerges as a local excitation in the condensed gauge boson field.

The model's renormalizability is discussed without assuming the Higgs Lagrangian.

Abstract

Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in the collision of massless Dirac fermions. Time in the relativistic many-body state should evolve while maintaining the direction of time in each particle, even if the particles are viewed from any inertial frames. This kinematical requirement leads to spontaneous symmetry breaking in the vacuum of these states, which gives a different meaning to the results of the Higgs model. In this vacuum, massless fermion-antifermion pairs and coherent collection of gauge bosons condense, which determine each other's mass. When a local excitation of the condensed gauge bosons propagates in space, a Higgs-like boson appears. The effective coupling of this Higgs-like boson to gauge bosons is calculated as a one-loop process. With this coupling, the total cross section of the pair annihilation of fermion and antifermion to gauge boson pair is calculated. Renormalizability of this model is discussed using the inductive method. Since the Higgs Lagrangian is not assumed, the divergence we must renormalize is only the logarithmic divergence, not the quadratic one.