Effective Sine(h)-Gordon-like equations for pair-condensates composed of bosonic or fermionic constituents

TL;DR

This paper develops an effective path integral formulation for super-symmetric pair condensates, transforming complex coset measures into Euclidean variables to facilitate classical and fluctuation analyses.

Contribution

It introduces a method to eliminate the nontrivial coset measure in super-symmetric pair condensate path integrals, enabling classical equations and fluctuation analysis in Euclidean variables.

Findings

Derived Euclidean path integration variables for pair condensates.

Formulated classical equations including higher-order fluctuations.

Provided a framework for analyzing super-symmetric pair condensates.

Abstract

An effective coherent state path integral for super-symmetric pair condensates is investigated with specification on the nontrivial coset integration measure. The nontrivial coset integration measure, determined by the square root of the super-determinant of the coset metric tensor, is eliminated by the inverse square root of this coset metric tensor; this results into Euclidean path integration variables for the pair condensate fields. According to the transformation to 'flat' anomalous path integration variables, first order variations of fields can be performed for classical equations with inclusion of second and higher even order variations for universal fluctuations determined by the coset metric tensor of the ortho-symplectic super-manifold.