Deformation Quantization, Quantization, and the Klein-Gordon Equation

TL;DR

This paper introduces Deformation Quantization (DQ) to physicists, compares it with other quantization methods, and formulates the Klein-Gordon equation within DQ, including new results on Fedosov star-products in specific space-times.

Contribution

It provides a basic introduction to DQ, compares it with canonical and path integral quantization, and presents original results on Fedosov star-products and the Klein-Gordon equation in de Sitter and anti-de Sitter spaces.

Findings

Construction of Fedosov star-product on dS and AdS space-times

Formulation of Klein-Gordon equation in DQ for these space-times

Discussion of convergence and operator ordering issues in DQ

Abstract

The aim of this proceeding is to give a basic introduction to Deformation Quantization (DQ) to physicists. We compare DQ to canonical quantization and path integral methods. It is described how certain issues such as the roles of associativity, covariance, dynamics, and operator orderings are understood in the context of DQ. Convergence issues in DQ are mentioned. Additionally, we formulate the Klein-Gordon (KG) equation in DQ. Original results are discussed which include the exact construction of the Fedosov star-product on the dS and AdS space-times. Also, the KG equation is written down for these space-times. This is a proceedings to the Second International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology.