Mathematical Quantization (Hardcover)

QUANTUM MECHANICS
Classical Physics
States and Events
Observables
Dynamics
Composite Systems
Quantum Computation
HILBERT SPACES
Definitions and Examples
Subspaces
Orthonormal Bases
Duals and Direct Sums
Tensor Products
Quantum Logic
OPERATORS
Unitaries and Projections
Continuous Functional Calculus
Borel Functional Calculus
Spectral Measures
The Bounded Spectral Theorem
Unbounded Operators
The Unbounded Spectral Theorem
Stone's Theorem
THE QUANTUM PLANE
Position and Momentum
The Tracial Representation
Bargmann-Segal Space
Quantum Complex Analysis
C*-ALGEBRAS
The Algebras C(X)
Topologies from Functions
Abelian C*-Algebras
The Quantum Plane
Quantum Tori
The GNS Construction
VON NEUMANN ALGEBRAS
The Algebras l8 (X)
The Algebras L8 (X)
Trace Class Operators
The Algebras B(H)
Von Neumann Algebras
The Quantum Plane and Tori
QUANTUM FIELD THEORY
Fock Space
CCR Algebras
Realtivistic Particles
Flat Spacetime
Curved Spacetime
OPERATOR SPACES
The Spaces V(K)
Mstiex Norms and Convexity
Duality
Matrix-Valued Functions
Operator Systems
HILBERT MODULES
Continuous Hilbert Bundles
Hilbert L8-Modules
Hilber C*-Modules
Hilbert W*-Modules
Crossed Products
Hilbert *-Bimodules
LIPSCHITZ ALGEBRAS
The Algebras Lip0(X)
Measurable Metrics
The Derivation Theorem
Examples
Quantum Markov Semigroups
QUANTUM GROUPS
Finite Dimensional C*-Algebras
Finite Quantum Groups
Compact Quantum Groups
Haar Measure\
REFERENCES