Chaotic Quantization of Four-Dimensional U(1) Lattice Gauge Theory

TL;DR

This paper shows that four-dimensional U(1) lattice gauge theory can be derived as a long-time limit of a classical five-dimensional gauge theory, linking quantum and classical descriptions through a specific energy scale.

Contribution

It introduces a novel approach connecting quantum U(1) lattice gauge theory to a classical higher-dimensional model, providing insights into quantization via classical dynamics.

Findings

Quantum theory emerges from classical dynamics in higher dimensions.

The Planck constant relates to classical energy and lattice parameters.

Long-time classical evolution reproduces quantum behavior.

Abstract

We demonstrate that the quantized U(1) lattice gauge theory in four Euclidean dimensions can be obtained as the long time limit of the corresponding classical U(1) gauge theory in 4+1 dimensions. The Planck constant hbar is related to the excitation energy and the lattice constant of this classical template.