The Yukawa Model in One Space - One Time Dimensions

TL;DR

This paper explores the Yukawa Model in a simplified one space-one time dimension, analyzing its classical constraints and applying Dirac quantization, then bosonizing to express the Hamiltonian in terms of scalar fields.

Contribution

It introduces a novel approach to quantize the Yukawa Model in low dimensions using Dirac's method and bosonization, differing from existing literature.

Findings

Classical system identified as constrained

Successful application of Dirac quantization method

Hamiltonian expressed via bosonization in scalar fields

Abstract

The Yukawa Model is revisited in one space - one time dimensions in an approach completely different to those available in the literature. We show that at the classical level it is a constrained system. We apply the Dirac method of quantization of constrained systems. Then by means of the bosonization procedure we uniformize the Hamiltonian at the quantum level in terms of a pseudo-scalar field and the chiral components of a real scalar field.