dorsal/arxiv
View SchemaMetrical Quantization
| Authors | John R. Klauder |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9804009 |
| URL | https://arxiv.org/abs/quant-ph/9804009 |
| DOI | 10.1007/BFb0105343 |
Abstract
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates. All quantization schemes that lead to Hilbert space vectors and Weyl operators---even those that eschew Cartesian coordinates---implicitly contain a metric on a flat phase space. This feature is demonstrated by studying the classical and quantum ``aggregations'', namely, the set of all facts and properties resident in all classical and quantum theories, respectively. Metrical quantization is an approach that elevates the flat phase space metric inherent in any canonical quantization to the level of a postulate. Far from being an unwanted structure, the flat phase space metric carries essential physical information. It is shown how the metric, when employed within a continuous-time regularization scheme, gives rise to an unambiguous quantization procedure that automatically leads to a canonical coherent state representation. Although attention in this paper is confined to canonical quantization we note that alternative, nonflat metrics may also be used, and they generally give rise to qualitatively different, noncanonical quantization schemes.
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"abstract": "Canonical quantization may be approached from several different starting\npoints. The usual approaches involve promotion of c-numbers to q-numbers, or\npath integral constructs, each of which generally succeeds only in Cartesian\ncoordinates. All quantization schemes that lead to Hilbert space vectors and\nWeyl operators---even those that eschew Cartesian coordinates---implicitly\ncontain a metric on a flat phase space. This feature is demonstrated by\nstudying the classical and quantum ``aggregations\u0027\u0027, namely, the set of all\nfacts and properties resident in all classical and quantum theories,\nrespectively. Metrical quantization is an approach that elevates the flat phase\nspace metric inherent in any canonical quantization to the level of a\npostulate. Far from being an unwanted structure, the flat phase space metric\ncarries essential physical information. It is shown how the metric, when\nemployed within a continuous-time regularization scheme, gives rise to an\nunambiguous quantization procedure that automatically leads to a canonical\ncoherent state representation. Although attention in this paper is confined to\ncanonical quantization we note that alternative, nonflat metrics may also be\nused, and they generally give rise to qualitatively different, noncanonical\nquantization schemes.",
"arxiv_id": "quant-ph/9804009",
"authors": [
"John R. Klauder"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1007/BFb0105343",
"title": "Metrical Quantization",
"url": "https://arxiv.org/abs/quant-ph/9804009"
},
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