A Unified Combination of Classical and Quantum Systems

TL;DR

This paper proposes a universal, model-independent framework to smoothly transition between classical and quantum descriptions, unifying them through natural integration procedures applicable to various systems including quantum gravity.

Contribution

It introduces a novel, straightforward method to connect classical and quantum systems universally, extending beyond traditional path integration techniques.

Findings

Unified procedure for classical-quantum transition

Applicability to spin, affine quantizations, and quantum gravity

Simplifies the connection between classical and quantum descriptions

Abstract

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a clear and continuous passage between the conventional distinction of either a strictly classical or a strictly quantized state. While path integration, among other procedures, provides an alternative route to connect classical and quantum expressions, it normally involves complicated, model-dependent, integrations. Our alternative procedures involve only model-independent procedures, and use more natural and straightforward integrations that are universal in kind. To introduce the basic procedures our presentation begins with familiar methods that are limited to basic, conventional, canonical quantum mechanical examples. In the final sections we illustrate how alternative quantization procedures, e.g., spin and affine quantizations, can also have smooth paths between classical and quantum stories, and with a few brief remarks, can also lead to similar stories for non-renormalizable covariant scalar fields as well as quantum gravity.