Self-Adjointness of Deformed Unbounded Operators

TL;DR

This paper investigates the self-adjointness of deformed unbounded operators using warped convolutions, establishing conditions for their self-adjointness and providing proofs within quantum mechanics and quantum field theory contexts.

Contribution

It introduces a novel approach to analyze the self-adjointness of deformed unbounded operators via warped convolutions and the Kato-Rellich theorem, with new proofs in quantum physics.

Findings

Deformed unbounded operators are self-adjoint under specific conditions.

The necessary condition for the oscillatory integral's well-definedness is identified.

Multiple proofs of self-adjointness are provided in quantum contexts.

Abstract

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.