
The Guest Editors for this special issue are
Alberto Cattaneo (Universität
Zürich, Switzerland)
Giuseppe Dito (Université de Bourgogne, Dijon, France)
Maxim Kontsevich (Institut des Hautes Études Scientifiques, BuressurYvette, France)
Daniel Sternheimer (Keio University, Yokohama, Japan)
The need for quantization was felt already around 1900, but quantum
mechanics proper started about 80 years ago. It then took half a century
to express in a mathematically and physically precise way what was
intuitively felt by many, that quantization is deformation. In the past
30 years what is now called “deformation quantization” developed and has
proved seminal in a variety of domains, from abstract mathematics to
modern theoretical physics.
The aim of this special “anniversary” issue is to present some
developments in that vast frontier area.
The issue contains 13 papers with the total of 315 pages.
We would like to thank all the authors who have published papers in
the issue, and to give our special thanks to all the referees for
providing constructive reviews.
The Guest Editors
Papers in this Issue:

Axiomatic Quantum Field Theory in Terms of Operator Product Expansions:
General Framework, and Perturbation Theory via Hochschild Cohomology

Stefan Hollands
SIGMA 5 (2009), 090, 45 pages [ abs
pdf ps ]

Deformation Quantization of Poisson Structures Associated to Lie Algebroids

Nikolai Neumaier and Stefan Waldmann
SIGMA 5 (2009), 074, 29 pages [ abs
pdf ps ]

Three Natural Generalizations of Fedosov Quantization

Klaus Bering
SIGMA 5 (2009), 036, 21 pages [ abs
pdf ps ]

Hochschild Cohomology and Deformations of CliffordWeyl Algebras

Ian M. Musson, Georges Pinczon and Rosane Ushirobira
SIGMA 5 (2009), 028, 27 pages [ abs
pdf ps ]

Toeplitz Quantization and Asymptotic Expansions: Geometric Construction

Miroslav Englis and Harald Upmeier
SIGMA 5 (2009), 021, 30 pages [ abs
pdf ps ]

Analyticity of the Free Energy of a Closed 3Manifold

Stavros Garoufalidis, Thang T.Q. Lê and Marcos Mariño
SIGMA 4 (2008), 080, 20 pages [ abs
pdf ps ]

Hochschild Cohomology Theories in White Noise Analysis

Rémi Léandre
SIGMA 4 (2008), 066, 13 pages [ abs
pdf ps ]

sl(2)Trivial Deformations of Vect_{Pol}(R)Modules of Symbols

Mabrouk Ben Ammar and Maha Boujelbene
SIGMA 4 (2008), 065, 19 pages [ abs
pdf ps ]

Hochschild Homology and Cohomology of Klein Surfaces

Frédéric Butin
SIGMA 4 (2008), 064, 26 pages [ abs
pdf ps ]

Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants

Damien Calaque and Carlo A. Rossi
SIGMA 4 (2008), 060, 17 pages [ abs
pdf ps ]

SpaceTime Diffeomorphisms in Noncommutative Gauge Theories

Marcos Rosenbaum, J. David Vergara and L. Román Juarez
SIGMA 4 (2008), 055, 21 pages [ abs
pdf ps ]

FieldTheoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

Reinhard Honegger, Alfred Rieckers and Lothar Schlafer
SIGMA 4 (2008), 047, 37 pages [ abs
pdf ps ]

Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology

José M. Isidro and Pedro Fernández de Córdoba
SIGMA 4 (2008), 040, 10 pages [ abs
pdf ps ]
 