States and representations in deformation quantization
نویسنده
چکیده
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]
منابع مشابه
Deformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملInduction of representations in deformation quantization
We discuss the procedure of Rieffel induction of representations in the framework of formal deformation quantization of Poisson manifolds. We focus on the central role played by algebraic notions of complete positivity.
متن کاملQuantum Half-Planes via Deformation Quantization
We give an idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real line. By an exact computation of the star-product and the operator ˆ̀Z , we show that the resulting representations exhausted all the irreducible representations of this groups.
متن کاملA Remark on the Deformation of GNS Representations of ∗ - Algebras
Motivated by deformation quantization we investigate the algebraic GNS construction of ∗representations of deformed ∗-algebras over ordered rings and compute their classical limit. The question if a GNS representation can be deformed leads to the deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann-Fock and the Schrödinger represe...
متن کاملQuasiclassical Calculations in Beam Dynamics
We present some applications of general harmonic/wavelet analysis approach (generalized coherent states, wavelet packets) to numerical/analytical calculations in (nonlinear) quasiclassical/quantum beam dynamics problems. (Naive) deformation quantization, multiresolution representations and Wigner transform are the key points.
متن کامل