Open AccessPosted Content
Noncommutative geometry and quantization
TL;DR: In this paper, the authors examine some recent developments in non-commutative geometry, including spin geometries on noncommutive tori and their quantization by the Shale-Stinespring procedure, and the emergence of Hopf algebras as a tool linking index theory and renormalization calculations.
read more
Abstract: We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a tool linking index theory and renormalization calculations
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Classical Theta Functions and Quantum Tori
TL;DR: The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function as mentioned in this paper, and the kernel satisfies a Schrodinger equation in which the role of time is played by the deformation parameter $\hbar$ and by a Poisson structure.
14
Convergence of Bogoliubov's Method of Renormalization in Momentum Spate
W. Zimmermann
- 01 Jan 2000
TL;DR: In this paper, the convergence of the Fcynman integrand is proved by an application of the power counting theorem, and the convergence is proved for the non-algebraic version of renormalization in momentum space.
References
String theory and noncommutative geometry
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this article, a non-zero B-field is introduced for string theory and the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and the corrections away from this limit are discussed.
5.4K
String Theory and Noncommutative Geometry
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this paper, a non-zero B-field is introduced for string theory and the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and the corrections away from this limit are discussed.
3.7K
•Book
Fundamentals of the Theory of Operator Algebras
Richard V. Kadison,John R. Ringrose +1 more
- 01 Jan 1983
TL;DR: In this article, the authors compare normal states and unitary equivalence of von Neumann algebras, including the trace and the trace trace of the trace of a projection.
3.1K
•Book
Trace ideals and their applications
Barry Simon
- 01 Jan 1979
TL;DR: In this paper, Calkin's theory of operator ideals and symmetrically normed ideals convergence theorems for trace, determinant, and Lidskii's theorem are discussed.
2.9K
Noncommutative Geometry and Matrix Theory: Compactification on Tori
Alain Connes,Michael R. Douglas,Michael R. Douglas,Albert Schwarz,Albert Schwarz,Albert Schwarz +5 more
TL;DR: In this article, the authors studied toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry, and argued that they correspond in supergravity to tori with constant background three-form tensor field.
1.6K