Gauge Theories on Open Lie Algebra Non-Commutative Spaces
A. Agarwal, L. Akant
TL;DR
This paper develops explicit star products for a class of non-commutative spaces defined by non-linear relations, formulates quantum gauge theories on these spaces, and details the Seiberg-Witten map.
Contribution
It provides explicit formulas for star products on certain non-commutative spaces and constructs quantum gauge theories including the Seiberg-Witten map.
Findings
Explicit star product formulas derived
Quantum gauge theories formulated on these spaces
Seiberg-Witten map explicitly constructed
Abstract
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of these star products is carried out. Quantum gauge theories are formulated on these spaces, and the Seiberg-Witten map is worked out in detail.
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