Noncommutative Structures in Mathematics and Physics

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Concise encyclopedia of supersymmetry : and noncommutative structures in mathematics and physics

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When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.

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The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally.

Noncommutative geometry and particle physics

This is the topic of chapter 3, by Christian Kassel. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required.

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An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity. An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here.

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The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples. This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory. EUR Add to basket. Cover Text This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.

A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. Product Type Book.

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Binding Hardcover. Publisher Springer Verlag GmbH.

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Publishing year Leites, V. Tensions in Supergravity Braneworlds; K. An Unconventional Supergravity; P. Grozman, D. Bergshoeff, et al. D-Branes and Vacuum Periodicity; D.

Cardona Guio, Alexander

Galtsov, V. Kosinski, et al. Leites, I. Noninvertibility, Semisupermanifolds and Categories Regularization; S. Duplij, W. Peeters, et al. Fedoruk, V.

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