Quantization, Coherent States, and Complex Structures

✍ Scribed by Daniel Canarutto, Arkadiusz Jadczyk, Marco Modugno (auth.), J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov, A. Odzijewicz (eds.)

• Publisher: Springer US
• Year: 1995
• Tongue: English
• Leaves: 289
• Edition: 1
• Category: Library

✦ Synopsis

The XIIIth Bialowieza Summer Workshop was held from July 9 to 15, 1994. While still within the general framework of Differential Geometric Methods in Physics, the XnIth Workshop was expanded in scope to include quantum groups, q-deformations and non-commutative geometry. It is expected that lectures on these topics will now become an integral part of future workshops. In the more traditional areas, lectures were devoted to topics in quantization, field theory, group representations, coherent states, complex and Poisson structures, the Berry phase, graded contractions and some infinite-dimensional systems. Those of us who have taken part in the evolution of the workshops over the years, feel a good measure of satisfaction with the excellent quality of the papers presented, in particular the mathematical rigour and novelty. Each year a significant number of new results are presented and future directions of research are discussed. Their freshness and immediacy inevitably leads to intense discussions and an exchange of ideas in an informal and physically charming environment. The present workshop also had a higher attendance than its predecessors, with ap­ proximately 65 registered participants. As usual, there was a large number of graduate students and young researchers among them.

✦ Table of Contents

Front Matter....Pages i-ix
Front Matter....Pages 1-1
On Quantum Mechanics in a Curved Spacetime with Absolute Time....Pages 3-19
Massless Spinning Particles on the Anti-De Sitter Spacetime....Pages 21-25
A Family of Nonlinear Schrödinger Equations: Linearizing Transformations and Resulting Structure....Pages 27-31
Modular Structures in Geometric Quantization....Pages 33-42
Diffeomorphism Groups and Anyon Fields....Pages 43-54
On a Full Quantization of the Torus....Pages 55-62
Differential Forms on the Skyrmion Bundle....Pages 63-71
Explicitly Covariant Algebraic Representations for Transitional Currents of Spin-1/2 Particles....Pages 73-78
The Quantum SU (2, 2)-Harmonic Oscillator....Pages 79-85
Geometro-Stochastic Quantization and Quantum Geometry....Pages 87-102
Prequantization....Pages 103-108
Classical Yang-Mills and Dirac Fields in the Minkowski Space and in a Bag....Pages 109-118
Symplectic Induction, Unitary Induction and BRST Theory (Summary)....Pages 119-119
Front Matter....Pages 121-121
Spin Coherent States for the Poincaré Group....Pages 123-129
Coherent States and Global Differential Geometry....Pages 131-140
Natural Transformations of Lagrangians into p -Forms on the Tangent Bundle....Pages 141-146
SL (2, ℝ)-Coherent States and Integrable Systems in Classical and Quantum Physics....Pages 147-158
Symplectic and Lagrangian Realization of Poisson Manifolds....Pages 159-171
From the Poincaré-Cartan Form to a Gerstenhaber Algebra of Poisson Brackets in Field Theory....Pages 173-183
Geometric Coherent States, Membranes, and Star Products....Pages 185-199
Front Matter....Pages 121-121
Integral Representation of Eigenfunctions and Coherent States for the Zeeman Effect....Pages 201-208
Front Matter....Pages 209-209
Quantum Coherent States and the Method of Orbits....Pages 211-216
On The Deformation of Commutation Relations....Pages 217-224
The q -Deformed Quantum Mechanics in the Coherent States Map Approach....Pages 225-231
Quantization by Quadratic Polynomials in Creation and Annihilation Operators....Pages 233-234
On Dirac Type Brackets....Pages 235-241
Quantum Trigonometry and Phase-Space Propensity....Pages 243-248
Noncommutative Space-Time Implied by Spin....Pages 249-255
Front Matter....Pages 257-257
Spectrum of the Dirac Operator on the SU(2) Manifold as Energy Spectrum for the Polyaniline Macromolecule....Pages 259-264
On Geometric Methods in the Description of Quantum Fluids....Pages 265-269
Galactic Dynamics in the Siegel Half-Plane....Pages 271-279
Graded Contractions of so (4, 2)....Pages 281-289
The Berry Phase and the Geometry of Coset Spaces....Pages 291-298
Back Matter....Pages 299-302

✦ Subjects

Applications of Mathematics;Theoretical, Mathematical and Computational Physics;Physics, general