Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Deformation Quantization

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 topics include:

• deformation quantization and algebraic geometry;
• deformation quantization methods in mathematics, including group theory;
• “higher structures” (goupoids, algebroids, operads, etc.) in deformation quantization;
• quantum groups in various flavors, viewed as deformations;
• noncommutative geometry, quantized spaces and strict deformation quantization;
• Toeplitz operators, pseudodifferential operators, index theorems, etc. in relation with deformation quantization;
• topological sigma models and their relation to deformation quantization;
• quantum field theory and string theory from the point of view of deformation quantization (including noncommutative quantum field theory);
• any applications of the above in mathematical and theoretical physics.

How to Submit an Article to the Issue.

The length of an article is not limited. Deadline for paper submission is October 1, 2008.

Publication will be done only on the results of the peer review according to refereeing policy of SIGMA.

If you have your paper ready earlier than the deadline, we encourage you to send it now. We will start the reviewing process and publish the paper as soon as the positive publication decision is made. The paper will be indexed in the relevant databases as soon as it is published without waiting for completion of the special issue.

Papers in this Issue:

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 ]

Forthcoming papers:

Hochschild Cohomology of Klein Surfaces
Frederic Butin