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.

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.]

References in corpus (1)

• Quantum Canonical Transformations: Physical Equivalence of Quantum Theories

Cited by in corpus (11)

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• Integrability vs Quantum Thermalization
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• Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
• Embedding of the Bosonic String into the $W_3$ String
• Non-Linear Canonical Transformations in Classical and Quantum Mechanics
• Non-Hermitian quantum canonical variables and the generalized ladder operators
• Implications of invariance of the Hamiltonian under canonical transformations in phase space
• Quantum Canonical Transformations revisited