We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

https://iopscience.iop.org/article/10.1088/1126-6708/1999/09/032/pdf

String theory and noncommutative geometry

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Noncommutative field theory

Quantum field theory on noncommutative spaces

Sphere Packings, Lattices and Groups

A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is described by the geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy. Investigation of the geometry and structure of such groups turns out to be useful for describing the global behavior of fluids for large time intervals.

Topological methods in hydrodynamics

In addition to the presentation speeches and the Nobel lectures, these volumes also provide brief biographies and the Nobel laureates' own accounts of their many years of preparation and effort that led to their achievements. The last decade of the twentieth century is already proving to be as dramatic as any decade before. The chances of global peace seem stronger now than at any time since 1900 and the people and organizations that have contributed most towards this progress are recognized by the Norwegian Nobel Committee. The Nobel Peace prizewinners during the period 1996 - 2000 include men, women and organizations whose principles, dedication and diligence continue to shape history. Below is a list of the prizewinners during the period 1996 - 2000. (1996) C F X BELO & J RAMOS-HORTA - for their work towards a just and peaceful solution to the conflict in East Timor; (1997) INTERNATIONAL CAMPAIGN TO BAN LANDMINES (ICBL) & J WILLIAMS - for their work for the banning and cleaning of anti-personnel mines; (1998) J HUME & D TRIMBLE - for their efforts to find a peaceful solution to the conflict in Northern Ireland; (1999) DOCTORS WITHOUT BORDERS - in recognition of the organization's pioneering humanitarian work on several continents; (2000) D J KIM - for his work for democracy and human rights in South Korea and in East Asia in general, and for peace and reconciliation with North Korea in particular.

Quantum mechanics in phase space : an overview with selected papers

Deforming Maps for Quantum Algebras

Torsion and geometrostasis in nonlinear sigma models

The Wigner phase-space distribution function provides the basis for Moyal{close_quote}s deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. The general features of time-independent Wigner functions are explored here, including the functional ({open_quotes}star{close_quotes}) eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux ({open_quotes}supersymmetric{close_quotes}) isospectral potential recursions; and their canonical transformations. These features are illustrated explicitly through simple solvable potentials: the harmonic oscillator, the linear potential, the P{umlt o}schl-Teller potential, and the Liouville potential. {copyright} {ital 1998} {ital The American Physical Society}

Cosmas K. Zachos

Papers

Quantum mechanics in phase space : an overview with selected papers

Deforming Maps for Quantum Algebras

Torsion and geometrostasis in nonlinear sigma models

Features of time-independent Wigner functions

Trigonometric structure constants for new infinite-dimensional algebras