dorsal/arxiv
View SchemaNon-Linear Canonical Transformations in Classical and Quantum Mechanics
| Authors | Alastair Brodlie |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401160 |
| URL | https://arxiv.org/abs/quant-ph/0401160 |
| DOI | 10.1063/1.1771482 |
Abstract
$p$-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.
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"abstract": "$p$-Mechanics is a consistent physical theory which describes both classical\nand quantum mechanics simultaneously through the representation theory of the\nHeisenberg group. In this paper we describe how non-linear canonical\ntransformations affect $p$-mechanical observables and states. Using this we\nshow how canonical transformations change a quantum mechanical system. We seek\nan operator on the set of $p$-mechanical observables which corresponds to the\nclassical canonical transformation. In order to do this we derive a set of\nintegral equations which when solved will give us the coherent state expansion\nof this operator. The motivation for these integral equations comes from the\nwork of Moshinsky and a variety of collaborators. We consider a number of\nexamples and discuss the use of these equations for non-bijective\ntransformations.",
"arxiv_id": "quant-ph/0401160",
"authors": [
"Alastair Brodlie"
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"doi": "10.1063/1.1771482",
"title": "Non-Linear Canonical Transformations in Classical and Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0401160"
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