States and representations in deformation quantization

Abstract

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.

51 pages, LaTeX2e, no figures

References in corpus (3)

• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
• The Picard groupoid in deformation quantization

Cited by in corpus (12)

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• Canonical transformations in quantum mechanics
• Quantization of Emergent Gravity
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Locally Noncommutative Space-Times
• Hermitian star products are completely positive deformations
• Quantum trajectories
• A Universal Construction of Universal Deformation Formulas, Drinfel'd Twists and their Positivity
• Classical Limits of Unbounded Quantities by Strict Quantization
• Deformation Quantization of a Certain Type of Open Systems
• QFT on homothetic Killing twist deformed curved spacetimes
• Quantization via Deformation of Prequantization