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, Bures-sur-Yvette, 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.

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 Clifford-Weyl 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 3-Manifold

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 ]

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

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

Field-Theoretic 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 ]