Abstract
We present the non-commutative extension of the U(N) Cremmer–Scherk–Kalb–Ramond theory, displaying its differential form and gauge structures. The Seiberg–Witten map of the model is also constructed up to 0(θ2).
Highlights
The first ideas about space-time noncommutativity were formulated by Heisenberg in the thirties [1], the first published work on the subject appeared in 1947 [2], introducing a possible framework for avoiding the characteristic singularities of quantum field theories
We propose a noncommutative generalization of the CSKR theory
We show that its covariant description, with the aid of differential forms, can be extended in order to incorporate Moyal products, characteristic of noncommutative field theories
Summary
The first ideas about space-time noncommutativity were formulated by Heisenberg in the thirties [1], the first published work on the subject appeared in 1947 [2], introducing a possible framework for avoiding the characteristic singularities of quantum field theories. The group multiplication is defined as a Moyal product In this way the symmetry structure of the noncommutative U (N ) theory is not the same as the corresponding commutative one and the group closure property is only achieved if the algebra generators close under commutations and under anticommutation. In place of g, ˆb and gdefined in (2.9), (2.12) and (2.13), we introduce the corresponding noncommutative forms These quantities present the following set of gauge transformations: δA = Dǫ δB = DΞ + i[ǫ ⋆, B] δG = i[Ξ ⋆, F ] + i[ǫ ⋆, G] δΩ = i[ǫ ⋆, Ω] − Ξ δF = i[ǫ ⋆, F ] δB = i[ǫ ⋆, B] δG = i[ǫ ⋆, G]. In what follows let us study the Seiberg-Witten map of the model, which presents some interesting features
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