Quantum physics as the projective representation theory of Noether symmetries

TL;DR

This paper introduces a novel quantization scheme based on projective representation theory of Noether symmetries, involving cohomological formulations and Taylor expansions around an observer's position, with implications for quantum physics.

Contribution

It develops a new quantization approach using cohomology and Taylor expansion of fields, extending the representation theory of Noether symmetries to include non-central extensions.

Findings

Constructs lowest-energy representations of extended Noether symmetry algebras.

Formulates classical physics via Koszul-Tate cohomology with fields and antifields.

Proposes a quantization scheme with a finite Taylor expansion, noting challenges in the limit.

Abstract

I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer's trajectory. This may be viewed as a new scheme for quantization. First classical physics is formulated as the cohomology of a certain Koszul-Tate (KT) complex, using not only fields and antifields but also their conjugate momenta. Then all fields are expanded in a Taylor series around the observer's present position, and terms of order higher than p are truncated. Finally, quantization is carried out by replacing Poisson brackets by commutators and imposing the KT cohomology in Fock space. This procedure is consistent for finite p, but the limit p\to\infty leads to difficulties.