Lie random fields

TL;DR

This paper develops the algebraic structure of Lie random fields, proving the vacuum state conjecture and showing they share many quantum properties despite differences in field commutator behavior.

Contribution

It extends the theory of Lie random fields, proving the vacuum state conjecture and analyzing their properties relative to quantum field algebras.

Findings

Vacuum vector defines a state over Lie random field algebra

Lie random fields share quantum properties like superposition and entanglement

Field commutator trivial at time-like separation

Abstract

The algebras of interacting "Lie random fields" that were introduced in J. Math. Phys. 48, 122302 (2007) are developed further. The conjecture that the vacuum vector defines a state over a Lie random field algebra is proved. The difference between Lie random field algebras and quantum field algebras is the triviality of the field commutator at time-like separation, the field commutator being trivial at space-like separation in both cases. Many properties that are usually taken to be specific to quantum theory, such as the superposition of states, entanglement, quantum fluctuations, and the violation of Bell inequalities, are also properties of Lie random fields.