{"title":"Time-Ordered Products and Exponentials","authors":"C. Lam","doi":"10.1201/9781003078296-27","DOIUrl":"https://doi.org/10.1201/9781003078296-27","url":null,"abstract":"I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.","PeriodicalId":409936,"journal":{"name":"Mathematical Methods of Quantum Physics","volume":"38 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120889353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Classical Properties of Generalized Coherent States: From Phase-Space Dynamics to Bell’s Inequality","authors":"C. Brif, A. Mann, M. Revzen","doi":"10.1201/9781003078296-23","DOIUrl":"https://doi.org/10.1201/9781003078296-23","url":null,"abstract":"We review classical properties of harmonic-oscillator coherent states. Then we discuss which of these classical properties are preserved under the group-theoretic generalization of coherent states. We prove that the generalized coherent states of quantum systems with Lie-group symmetries are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell's inequality upon splitting.","PeriodicalId":409936,"journal":{"name":"Mathematical Methods of Quantum Physics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126595007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Introduction to Coordinate Free Quantization and its Application to Constrained Systems 1","authors":"J. Klauder, S. Shabanov","doi":"10.1201/9781003078296-14","DOIUrl":"https://doi.org/10.1201/9781003078296-14","url":null,"abstract":"Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat phase space metric can be incorporated into a covariant, coordinate-free quantization procedure involving a continuous-time (Wiener measure) regularization of traditional phase space path integrals. Additionally we show how such procedures can be extended to incorporate systems with constraints and illustrate that extension for special systems.","PeriodicalId":409936,"journal":{"name":"Mathematical Methods of Quantum Physics","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133894642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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