p-mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how nonlinear canonical transformations affect p-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of p-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.p-mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how nonlinear canonical transformations affect p-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of p-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.

arXiv:quant-ph/0401160Journal of Mathematical PhysicsJul 9, 20044 citations

Non-Linear Canonical Transformations in Classical and Quantum Mechanics

Alastair Brodlie

$p$ -Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$ -mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$ -mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.

Jan 26, 20046 citations

Canonical Transformations in Quantum Mechanics

A. Anderson

arXiv:hep-th/9305054Annals of PhysicsJun 1, 199490 citations

Canonical transformations and their representations in quantum mechanics

M. Moshińsky

Lecture notes in mathematicsJan 1, 19771 citation

p

-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect

p

-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of

p

-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.