Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics

TL;DR

This paper develops a statistical thermodynamics framework for a non-commutative special relativity, leading to a generalized quantum dynamics where space and time are operator-valued, aiming to describe quantum field theory without classical time dependence.

Contribution

It introduces a novel thermodynamic approach based on Trace Dynamics to derive a generalized quantum dynamics from non-commutative space-time and matter degrees of freedom.

Findings

Derivation of a generalized quantum dynamics from non-commutative special relativity.

Demonstration that space and time can be operator-valued in this framework.

Foundation for a quantum theory independent of classical space-time background.

Abstract

There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here.