Formal GNS Construction and States in Deformation Quantization
نویسندگان
چکیده
منابع مشابه
Locality in GNS Representations of Deformation Quantization
In the framework of deformation quantization we apply the formal GNS construction to find representations of the deformed algebras in pre-Hilbert spaces over C[[λ]] and establish the notion of local operators in these pre-Hilbert spaces. The commutant within the local operators is used to distinguish ‘thermal’ from ‘pure’ representations. The computation of the local commutant is exemplified in...
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In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction. But also Rieffel induction of representations as well as strong Morita equivalence, the Dirac monopole and the strong Picard groupoid are discussed. E-mail: [email protected]...
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1. INTRODUCTION Quantum mechanics is often distinguished from classical mechanics by a statement to the effect that the observables in quantum mechanics, unlike those in classical mechanics, do not commute with one another. Yet classical mechanics is meant to give a description (with less precision) of the same physical world as is described by quantum mechanics. One mathematical transcription ...
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This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and prePoisson submanifolds, their appearance as branes of the PSM, quantization in terms of L∞and A∞-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This le...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1998
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050402