A quantum-classical duality and emergent space-time

TL;DR

This paper establishes a duality between quantum spinor systems and classical scalar models, revealing how classical space-time may emerge from quantum operator properties through a novel duality framework.

Contribution

It introduces a quantum-classical duality that preserves locality and links the classical measure to relativistic Green's functions, suggesting a mechanism for space-time emergence.

Findings

Dual classical partition function derived from quantum spinors.

Locality structure preserved in the dual classical system.

Classical measure expressed via relativistic Green's functions.

Abstract

We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a model on 2-sphere configuration space), but the locality structure of the dual system is preserved, in contrast to the imaginary time formalism. We also show that the measure of integration in the classical partition function can be formally expressed through relativistic Green's functions which suggests a possible mechanism for the emergence of a classical space-time from anti-commutativity of quantum operators.