Generalized Fock space and contextuality

TL;DR

This paper introduces a generalized Fock space framework for representing contextual probabilities, enabling the use of creation and annihilation operators to analyze probabilistic dynamics and reproduce classical kinetic equations.

Contribution

It extends the Fock space formalism to include contextual probabilities and quantifies context-dependence using an interference term in the total probability formula.

Findings

Reproduces the Doi-Peliti formalism within the generalized Fock space

Provides a method to quantify contextuality via interference terms

Links probabilistic dynamics with creation and annihilation operator calculus

Abstract

This paper is devoted to linear space representations of contextual probabilities - in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way we reproduce the Doi-Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability - by the magnitude of the interference term.