Quantum Canonical Transformations and Integrability: Beyond Unitary Transformations
Abstract
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A definition of quantum integrability in terms of canonical transformations is proposed which includes systems which have fewer commuting integrals of motion than degrees of freedom. The important role of non-unitary transformations in integrability is discussed.
Cite
@article{arxiv.hep-th/9302061,
title = {Quantum Canonical Transformations and Integrability: Beyond Unitary Transformations},
author = {Arlen Anderson},
journal= {arXiv preprint arXiv:hep-th/9302061},
year = {2010}
}
Comments
15 pages, LaTeX, Imperial-TP-92-93-19 [Revision consists of new material on observables and an explanation of how the proposed definition of integrability allows for systems which have fewer commuting integrals of the motion than degrees of freedom.]