Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics

Abstract

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space localization. The reader is supposed to know elementary functional analysis and quantum mechanics.

89 pages

Cited by in corpus (22)

• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Decoherence-Free Subspaces and Subsystems
• Stabilizing Quantum Information
• Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies
• Topological Protection and Quantum Noiseless Subsystems
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
• From Symmetries to Commutant Algebras in Standard Hamiltonians
• Noncommutative geometry, gauge theory and renormalization
• Decoherence, Control, and Symmetry in Quantum Computers
• Structure and properties of the algebra of partially transposed permutation operators
• A Spectral Theorem for Imprimitivity C*-bimodules
• Quantum Mechanics With Noncommutative Amplitudes
• Functional Mellin Transforms
• Noncommutative Geometry and Quantum Group Symmetries
• Some convolution products in Quantum Field Theory
• Toward the construction of a C^* algebra in string field theory
• Quantum Fourier Transform in a Decoherence-Free Subspace
• Could a Classical Probability Theory Describe Quantum Systems?
• Induced representations of locally C*-algebras
• Kähler geometry on complex projective spaces via reduction and unfolding
• Convolution product construction of interactions in probabilistic physical models
• K-theory in cutoff version of Vacuum String Field Theory