Dynamical Symmetry Breaking of a Relativistic Model in Quasi-(1+1)-Dimensions. I. Formulation

TL;DR

This paper formulates a relativistic quasi-(1+1)-dimensional model to study dynamical symmetry breaking, mass generation, and superconductivity, revealing phase transitions relevant to condensed matter systems.

Contribution

It introduces a novel relativistic framework with nonlocal interactions to analyze symmetry breaking and superconductivity in quasi-one-dimensional systems.

Findings

Dynamical generation of Dirac mass term.

Identification of metal-insulator and superconductor phase transitions.

Application of generalized BCS interactions to relativistic models.

Abstract

The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativistic model is investigated. The motions of particles in intrachain are described as a relativistic electron-hole gas, while the interchain hopping term is introduced as a 0th-component of vector in (1+1)-dimensions, a kind of chemical potential of the system. The gauge symmetry of the model is chosen as U(1) suitable for a possible situation of a real substance in condensed matter physics. We consider the BCS-type contact interactions for the s-wave fermion-pair condensates, while employ the nonlocal interactions of the generalized BCS framework to generate the $p$-, $d$- and $f$-wave condensations in the system. Especially we examine the dynamical generation of a Dirac mass term and superconductivity in the model. The phenomenon is interpreted as metal-insulator/metal-superconductor phase transitions.