Resurgent Deformation Quantisation

TL;DR

This paper develops a new algebraic framework for deformation quantisation using resurgent analysis, enabling the capture of quantum effects beyond traditional methods through integral formulas for resurgent operators.

Contribution

It introduces a resurgent deformation algebra based on analytic continuation, expanding the scope of quantum effects modeled in deformation quantisation.

Findings

Constructed a complex Heisenberg algebra with resurgent operators.

Derived an integral formula for the product of resurgent operators.

Proposed an algebraic structure capturing quantum effects beyond formal deformation.

Abstract

We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation.