`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

TL;DR

This paper introduces a novel background-independent third quantization framework for vacuum Einstein gravity and free Yang-Mills theories, utilizing sheaf-theoretic and cohomological methods within Abstract Differential Geometry.

Contribution

It develops a fully covariant, functorial third quantization scheme based on algebraico-categorical tools, advancing quantum gravity research beyond traditional approaches.

Findings

Provides a background-independent quantization method

Ensures full covariance through functorial procedures

Discusses implications for current and future quantum gravity research

Abstract

Based on the algebraico-categorical (:sheaf-theoretic and sheaf cohomological) conceptual and technical machinery of Abstract Differential Geometry, a new, genuinely background spacetime manifold independent, field quantization scenario for vacuum Einstein gravity and free Yang-Mills theories is introduced. The scheme is coined `third quantization' and, although it formally appears to follow a canonical route, it is fully covariant, because it is an expressly functorial `procedure'. Various current and future Quantum Gravity research issues are discussed under the light of 3rd-quantization. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.