Boson-Fermion unification implemented by Wick calculus

TL;DR

This paper introduces a super-symmetric transformation between Bose and Fermi Fock spaces using Wick calculus, generalizing quantum stochastic calculus to include spectral splitting of the one-particle space.

Contribution

It develops a novel Wick calculus framework that unifies bosonic and fermionic fields via spectral splitting and super-symmetric transformations.

Findings

Constructed a super-symmetric transformation between Bose and Fermi Fock spaces.

Developed a generalized Wick calculus for integration over internal spaces.

Extended quantum stochastic calculus to include spectral splitting of the one-particle space.

Abstract

We construct a transformation between Bose Fock space and Fermi Fock space that is super-symmetric in the sense that it converts Boson fields into Fermi fields over a fixed one-particle space. The transformation involves the spectral splitting of the one-particle space into a continuous direct integral of internal spaces. We present a theory of integration on the Fock spaces over the square intergable functions taking values in these internal spaces which we refer to as a Wick calculus: this is a natural generalization of the theory of quantum stochastic calculus which used a single fixed internal space.