Soliton Solutions on Noncommutative Orbifold $T^{2N}/G$

Details Soliton Solutions on Noncommutative Orbifold $T^{2N}/G$ Soliton Solutions on Noncommutative Orbifold $T^{2N}/G$

2004-05-14

arxiv.org/abs/hep-th/0405130v1

Physics

High Energy Physics

High Energy Physics - Theory

31 pages

Scientific paper

In this paper, we construct the common eigenstates of "translation" operators $\{U_{s}\}$ and establish the generalized $Kq$ representation on integral noncommutative torus $T^{2N}$. We then study the finite rotation group $G$ in noncommutative space as a mapping in the $Kq$ representation and prove a Blocking Theorem. We finally obtain the complete set of projection operators on the integral noncommutative orbifold $T^{2N}/G$ in terms of the generalized $Kq$ representation. Since projectors are soliton solutions on noncommutative space in the limit $\alpha ^{\prime}B_{ij}\to \infty (\Theta_{ij}/\alpha ^{\prime}\to 0)$, we thus obtain all soliton solutions on that orbifold $T^{2N}/G$.

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