Gauge Theories beyond Gauge Theories

✍ Scribed by Julius Wess

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 96 KB
• Volume: 49
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/1521-3978(200105)49:4/6<377::aid-prop377>3.0.co;2-2

✦ Synopsis

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 Å 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.