Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-10-23
JHEP 0012 (2000) 008
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, minor changes to text, references added
Scientific paper
10.1088/1126-6708/2000/12/008
Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In U(1) gauge theories, we note that these generalized *-products occur in the expansion of some quantities that are invariant under noncommutative gauge transformations, but contain an infinite number of powers of the noncommutative gauge field. One example is an open Wilson line. Another is the expression for a commutative field strength tensor in terms of the noncommutative gauge field. Seiberg and Witten derived differential equations that relate commutative and noncommutative gauge transformations, gauge fields and field strengths. In the U(1) case we solve these equations neglecting terms of fourth order in the gauge field but keeping all orders in the noncommutative parameter.
Mehen Thomas
Wise Mark B.
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