On the ground state of a free massless (pseudo)scalar field in two dimensions

TL;DR

This paper analyzes the ground state of a free massless (pseudo)scalar field in two dimensions, showing it can be represented as a tensor product of vacuum and zero-mode wave functions, and relates it to the bosonized BCS wave function of the Thirring model.

Contribution

It demonstrates that the ground state can be expressed as a tensor product of vacuum and zero-mode states and connects this to the bosonized BCS wave function of the Thirring model.

Findings

Ground state represented as tensor product of vacuum and zero-mode

Connection established between the ground state and bosonized BCS wave function

Ground state description consistent with infrared divergence-free quantum field theory

Abstract

We investigate the ground state of a free massless (pseudo)scalar field in 1+1-dimensional space-time. We argue that in the quantum field theory of a free massless (pseudo)scalar field without infrared divergences (Eur. Phys. J. C24, 653 (2002)) the ground state can be represented by a tensor product of wave functions of the fiducial vacuum and of the collective zero-mode, describing the motion of the ``center of mass'' of a free massless (pseudo)scalar field. We show that the bosonized version of the BCS wave function of the ground state of the massless Thirring model obtained in (Phys.Lett. B563, 231 (2003)) describes the ground state of the free massless (pseudo)scalar field.