Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
نویسنده
چکیده
A detailed description of the infinite-dimensional Lie algebra of ⋆-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C∗-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
منابع مشابه
BV-Quantization of a Noncommutative Yang–Mills Theory Toy Model
We review the Batalin-Vilkovisky quantization procedure for Yang–Mills theory on a 2-point space. 1) Talk given at the 5-th International Conference ”Renormalization Group 2002”, Tatranska Strba, Slovakia, March 10-16, 2002 2) Email: [email protected] 1 In this talk we give a short summary of [1], where we proposed the quantization of one of the simplest toy models for noncommutative...
متن کاملString Geometry and the Noncommutative Torus
We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra A and the noncommutative torus. We show that the tachyon algebra of A is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of function...
متن کاملar X iv : h ep - t h / 00 12 14 5 v 3 2 9 Ju l 2 00 1 Introduction to M ( atrix ) theory and noncommutative geometry
Noncommutative geometry is based on an idea that an associative algebra can be regarded as " an algebra of functions on a noncommutative space ". The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang-Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was f...
متن کاملJa n 20 01 Introduction to M ( atrix ) theory and noncommutative geometry
Noncommutative geometry is based on an idea that an associative algebra can be regarded as " an algebra of functions on a noncommutative space ". The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang-Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was f...
متن کامل2 00 0 Electromagnetism and Gauge Theory on the Permutation Group S
Using noncommutative geometry we do U(1) gauge theory on the permutation group S 3. Unlike usual lattice gauge theories the use of a nonAbelian group here as spacetime corresponds to a background Riemannian curvature. In this background we solve spin 0, 1/2 and spin 1 equations of motion, including the spin 1 or 'photon' case in the presence of sources, i.e. a theory of classical electromagneti...
متن کامل