---
title: "The Weyl Representation in Classical and Quantum Mechanics • CBPF Index"
description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community."
canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb89d"
locale: en
meta:
  "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community."
  "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_The%2BWeyl%2BRepresentation%2Bin%2BClassical%2Band%2BQuantum%2BMechanics%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_A.%2BM.%2BOzorio%2Bde%2BAlmeida%2Cdetalhe_1996%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI4OWQi%2Cs_Tohw7yaSS9VHN8sr.png"
  "og:image:height": "600"
  "og:image:type": image/png
  "og:image:width": "1200"
  "og:title": "The Weyl Representation in Classical and Quantum Mechanics • CBPF Index"
  "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_The%2BWeyl%2BRepresentation%2Bin%2BClassical%2Band%2BQuantum%2BMechanics%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_A.%2BM.%2BOzorio%2Bde%2BAlmeida%2Cdetalhe_1996%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI4OWQi%2Cs_Tohw7yaSS9VHN8sr.png"
---

> Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt)

**Physics Note****Published**

# **The Weyl Representation in Classical and Quantum Mechanics**

**A. M. Ozorio de Almeida**

1996

[**Download PDF **0.7 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb89d/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=The%20Weyl%20Representation%20in%20Classical%20and%20Quantum%20Mechanics)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>A. M. Ozorio de Almeida</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>1996</dd>

<dt>Description</dt>
<dd>The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation is connected to new generating functions described by chords and centres in phase space. Both classical and quantal theories relie on the group of translations and reflections through a point in phase space. The composition of small time evolutions leads to new versions of the classical variational principle and to path integrals in quantum mechanics. The strong resemblance between the two theories allows a clear derivation of the semiclassical limit in which observables evolve classically in the Weyl representation. The restriction of the motion to the energy shell in classical mechanics is the basis for a full review of the semiclassical Wigner function and the theory of scars of periodic orbits. By embedding the theory of scars in a fully uniform approximation, it is shown that the region in which the scar contribution is oscillatory is separated from a decaying region by a caustic that touches the shell along the periodic orbit and widens quadratically within the energy shell.</dd>

<dt>Year</dt>
<dd>1996</dd>

<dt>Number</dt>
<dd>CBPF-NF-062/96</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

```json
{"@context":"https://schema.org","@graph":[{"@id":"https://index.cbpf.br/en#website","@type":"WebSite","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","inLanguage":"en-US","name":"CBPF Index","url":"https://index.cbpf.br/en","publisher":{"@id":"https://index.cbpf.br/#identity"},"translationOfWork":{"@id":"https://index.cbpf.br/#website"}},{"@id":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb89d#webpage","@type":"WebPage","description":"CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community.","name":"The Weyl Representation in Classical and Quantum Mechanics","url":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb89d","isPartOf":{"@id":"https://index.cbpf.br/en#website"},"potentialAction":[{"@type":"ReadAction","target":["https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb89d"]}],"primaryImageOfPage":{"@id":"https://index.cbpf.br/#logo"}},{"@id":"https://index.cbpf.br/#identity","@type":"Organization","alternateName":"CBPF","description":"Unidade de pesquisa do Ministério da Ciência, Tecnologia e Inovação dedicada à pesquisa básica em Física, suas aplicações e à formação científica.","email":"web@cbpf.br","legalName":"Centro Brasileiro de Pesquisas Físicas/CBPF","name":"Centro Brasileiro de Pesquisas Físicas","taxID":"04.044.443/0001-35","telephone":"+55-21-2141-7100","url":"https://cbpf.br","address":{"@type":"PostalAddress","streetAddress":"Rua Dr. Xavier Sigaud, 150","addressLocality":"Rio de Janeiro","addressRegion":"RJ","postalCode":"22290-180","addressCountry":"BR"},"logo":{"@id":"https://index.cbpf.br/#logo"},"sameAs":["https://twitter.com/cbpf_mcti"]},{"@id":"https://index.cbpf.br/#logo","@type":"ImageObject","caption":"Centro Brasileiro de Pesquisas Físicas","contentUrl":"https://index.cbpf.br/icon-512x512-light.png","inLanguage":"en-US","url":"https://index.cbpf.br/icon-512x512-light.png"}]}
```

## Sitemap

See the full [sitemap](https://index.cbpf.br/sitemap.md) for all pages.