A Classical Analogue to the Standard Model, Chapter 1: Normalisable quasiparticles on a manifold with anticommuting co-ordinates

TL;DR

This paper presents a classical model of free fields on a manifold with anticommuting coordinates that emulates a five-species quantum field theory, highlighting novel classical-quantum analogies in superspace.

Contribution

It introduces a new classical model on superspace with anticommuting coordinates that reproduces complex quantum field behavior, expanding the understanding of quasiparticles in such manifolds.

Findings

Model emulates a five-species interacting quantum field theory.

Lagrangian derived solely from anticommutation properties.

Part of a series connecting classical models to quantum phenomena.

Abstract

Quasiparticles and analog models are ubiquitous in the study of physical systems. Little has been written about quasiparticles on manifolds with anticommuting co-ordinates, yet they are capable of emulating a surprising range of physical phenomena. This paper introduces a classical model of free fields on a manifold with anticommuting co-ordinates, identifies the region of superspace which the model inhabits, and shows that the model emulates the behaviour of a five-species interacting quantum field theory on $\mathbb{R}^{1,3}$. The Lagrangian of this model arises entirely from the anticommutation property of the manifold co-ordinates. This is part one of a series, which continues in arXiv:2108.07719 and arXiv:0805.3819, and concludes in arXiv:2008.05893 with a first-principles calculation of the value of the gravitational constant in the classical analogue model.