A relativistic statistical field theory on a discretized Minkowski lattice with quantum-like observables

TL;DR

This paper develops a relativistic statistical field theory on a discretized Minkowski lattice, constructing a quantum-like operator framework with non-commuting field operators that satisfy microcausality.

Contribution

It introduces a novel relativistic statistical field theory with a quantum-like operator structure on a discretized Minkowski lattice, including a new Hilbert space and Fock space formulation.

Findings

Field operators exhibit quantum-like properties.

Operators do not commute in general.

Microcausality condition is satisfied in free field theory.

Abstract

A relativistic statistical field theory is constructed for a fluctuating complex-valued scalar field on a discretized Minkowski lattice. A Hilbert space of observables is then constructed from functionals of the fluctuating complex-valued scalar field with an inner product defined in terms of expectation values of the functionals. A bosonic Fock space is then constructed from the Hilbert space and creation and annihilation operators that act on the Fock space are defined. The creation and annihilation operators are used to define field operators. These field operators have some interesting quantum-like properties. For example, the field operators do not commute in general and, in the particular case of the free field theory, can be shown to satisfy the microcausality condition.