Deformation quantization on jet manifolds

TL;DR

This paper extends the theory of deformation quantization by utilizing jet manifold techniques to formulate multidifferential operators and their infinite order jet prolongations, leading to a covariant star-product expression.

Contribution

It introduces a jet manifold-based formulation for multidifferential operators in deformation quantization, including their infinite order prolongation with a canonical flat connection.

Findings

Extended deformation quantization to jet manifolds.

Derived covariant formula for star-product.

Unified differential operator framework.

Abstract

Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the multidifferential ones, and consider their infinite order jet prolongation. The infinite order jet manifold is endowed with the canonical flat connection that provides the covariant formula of a deformation star-product.