Thick morphisms of supermanifolds and oscillatory integral operators

TL;DR

This paper introduces quantum thick morphisms as oscillatory integral operators and demonstrates that classical thick morphisms are their limits, advancing the understanding of morphisms in supermanifold theory.

Contribution

It defines quantum thick morphisms via oscillatory integrals and establishes their connection as limits to classical thick morphisms, expanding the framework of supermanifold morphisms.

Findings

Quantum thick morphisms are particular oscillatory integral operators.

Classical thick morphisms are shown to be limits of quantum thick morphisms.

Abstract

We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of `quantum thick morphisms' defined here as particular oscillatory integral operators on functions.