Parent-bilinear Sea-boson Correspondence with Spin

TL;DR

This paper provides a detailed tutorial on deriving the correspondence between fermionic/bosonic fields with spin and sea/condensate displacements, incorporating finite temperature effects via inhomogeneous chemical potential, and reproducing key features of the free theory.

Contribution

It introduces a detailed derivation of the spin-dependent sea-boson correspondence including finite temperature effects with inhomogeneous chemical potential.

Findings

Salient features of the free theory are reproduced.

Formulas for sea-bosons are provided.

Finite temperature Fermi correlators are computed.

Abstract

This is a sort of tutorial where we present many of the tedious details involved in deriving the correspondence between the number conserving product of two fermi/bose fields with spin and the corresponding sea/condensate displacements also with spin. This time we include finite temperature effects differently by coupling the sea-bosons to an inhomogeneous chemical potential. It is shown that many of the salient features of the free theory are reproduced properly by this approach. An attempt is made to be as detailed as possible, this includes providing formulas for the sea-bosons as well as computing the finite temperature Fermi correlators.