Cohomology and Bessel functions Theory

TL;DR

This paper explores the connection between cohomological quantum mechanics on the punctured plane and Bessel functions, establishing correspondence rules that recover and generate formulas in Bessel functions theory.

Contribution

It introduces a novel link between cohomological quantum mechanics and Bessel functions, leading to new formulas and insights in Bessel functions theory.

Findings

Identification of Bessel functions with homotopic loops on the plane

Development of correspondence rules between exponentials and Bessel functions

Derivation of new formulas in Bessel functions theory

Abstract

By studying cohomological quantum mechanics on the punctured plane,we were led to identify (reduced) Bessel functions with homotopic loops living on the plane.This identification led us to correspondence rules between exponentials and Bessel functions.The use of these rules makes us retrieve known but also new formulas in Bessel functions theory.