We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi sa...We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor展开更多
This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are...This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are similar, where A1, A2, B1, B2 are first-order differential （difference） operators. The main step in the algorithm is to find a rational solution of a parametric differential （difference） Risch＇s equation, which has been well-studied in symbolic integration （summation）.展开更多
基金the Talent Introduction Project of Xianyang Normal University under Grant No.07XSYK217
文摘We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor
基金supported by a 973 key project under Grant No.2004CB318000the National Natural Science Foundation under Grant No.76596100
文摘This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are similar, where A1, A2, B1, B2 are first-order differential （difference） operators. The main step in the algorithm is to find a rational solution of a parametric differential （difference） Risch＇s equation, which has been well-studied in symbolic integration （summation）.
