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Gauge Theories beyond Gauge Theories
Author(s) -
Wess Julius
Publication year - 2001
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200105)49:4/6<377::aid-prop377>3.0.co;2-2
Subject(s) - introduction to gauge theory , supersymmetric gauge theory , brst quantization , quantum gauge theory , gauge anomaly , algebra over a field , hamiltonian lattice gauge theory , gauge theory , mathematics , gauge covariant derivative , isomorphism (crystallography) , pure mathematics , mathematical descriptions of the electromagnetic field , gauge fixing , physics , gauge boson , mathematical physics , crystal structure , chemistry , crystallography
We introduce the algebra of functions generated by non‐commuting coordinates and construct an isomorphism of this algebra to the usual algebra of functions equipped with a non‐commutative ♦ product. In order to be able to formulate dynamics and do field theory, we have to define derivatives and integration. The construction of non‐abelian gauge theory on non‐commutative spaces is based on enveloping algebra‐valued gauge fields. The number of independent field components is reduced to the number of gauge fields in a usual gauge theory. This is done with the help of the Seiberg‐Witten map.