Soliton solutions on noncommutative orbifold \(T^ 2/Z_ 4\). (English) Zbl 1070.81104
Summary: In this paper, we explicitly construct a series of projectors on integrable noncommutative orbifold \(T^2/Z_4\) by extended \(GHS\) construction. They include integration of two arbitary functions with \(Z_4\) symmetry. Our expression possesses manifest \(Z_4\) symmetry. It is proven that the expression includes all projectors with minimal trace and in their standard expansions, the eigenvalue functions of coefficient operators are continuous with respect to the arguments \(k\) and \(q\). Based on the integral expression, we alternately show the derivative expression in terms of the similar kernel to the integral one. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons.
MSC:
| 81T75 | Noncommutative geometry methods in quantum field theory |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
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