On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

TL;DR

This paper constructs a consistent 1+1D quantum field theory for a free massless (pseudo)scalar field, demonstrating spontaneous symmetry breaking and the emergence of Goldstone bosons without infrared divergences.

Contribution

It provides a novel construction of a free massless (pseudo)scalar quantum field theory in 1+1 dimensions that avoids infrared divergences and confirms spontaneous symmetry breaking.

Findings

Spontaneous breaking of continuous symmetry in the model.

Goldstone bosons identified as quanta of the scalar field.

Verification of key inequalities related to the Mermin-Wagner-Hohenberg theorem.

Abstract

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that a continuous symmetry of (pseudo)scalar field translations is spontaneously broken. Goldstone bosons appear as quanta of a free massless (pseudo)scalar field. We show that the main inequality between vacuum expectation values of certain operators which has been used for the derivation of the Mermin-Wagner-Hohenberg theorem is fulfilled in the quantum field theory of a free massless (pseudo)scalar field free of infrared divergences.