GROUP QUANTIZATION ON CONFIGURATION SPACE

TL;DR

This paper advances the Group Approach to Quantization by enabling symmetry group construction directly on configuration space without explicit phase space knowledge, demonstrated on fields in curved spacetime and electromagnetic backgrounds.

Contribution

It introduces a method to construct the quantizing group directly on configuration space, bypassing the need for explicit phase space solutions, applicable to various field theories.

Findings

Constructed symmetry groups for conformally invariant fields.

Extended the method to include non-abelian groups like Kac-Moody.

Applicable to fields in curved spacetime and electromagnetic interactions.

Abstract

New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the "quantizing group") does not require, in general, the explicit construction of the phase space of the system, i.e., does not require the actual knowledgement of the general solution of the classical equations of motion: in many relevant cases an implicit construction of the group can be given, directly, on configuration space. As an application we construct the symmetry group for the conformally invariant massless scalar and electromagnetic fields and the scalar and Dirac fields evolving in a symmetric curved space- time or interacting with symmetric classical electromagnetic fields. Further generalizations of the present procedure are also discussed and in particular the conditions under which non-abelian (mainly Kac-Moody) groups can be included.