Composite boson dominance in relativistic field theories

TL;DR

This paper introduces a bosonization technique for relativistic fermion theories, deriving an effective bosonic action that respects symmetries and reproduces known results in large flavor limits, with applications to gauge theories.

Contribution

It presents a new bosonization method for relativistic fermion theories that maintains symmetries and accurately captures bosonic condensates, including their structure functions.

Findings

Reproduces exact bosonic sector results in large N_f limit.

Identifies the structure function of the condensed composite as similar to BCS Cooper pairs.

Demonstrates applicability to gauge theories using lattice regularization.

Abstract

We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries, including gauge invariance, with the exception of Euclidean invariance which must be checked a posteriori. We use a lattice regularization which should make applications to gauge theories easier. We test the method on a fermion field theory with quartic interaction in the limit when the number of flavours N_f is large, and show that it reproduces the exact results in the bosonic sector, namely condensation of a compositeboson with the right mass which breaks the discrete chiral invariance of the model. Moreover we determine the structure function of the condensed composite, whose spatial part turns out to be identical to that of the Cooper pairs of the BCS model of superconductivity.