Theta functions on noncommutative T^{4}
Abstract
We construct the socalled theta vectors on noncommutative T^{4}, which correspond to the theta functions on commutative tori with complex structures. Following the method of Dieng and Schwarz, we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions, the theta vectors. The holomorphic structure in the noncommutative T^{4} case is given by a 2×2 complex matrix, and the consistency requires its offdiagonal elements to be the same. We also construct the tensor product of these functions satisfying the consistency requirement.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2004
 DOI:
 10.1063/1.1629778
 arXiv:
 arXiv:hepth/0303091
 Bibcode:
 2004JMP....45..461K
 Keywords:

 11.25.Mj;
 11.10.z;
 02.10.Yn;
 Compactification and fourdimensional models;
 Field theory;
 Matrix theory;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 17 pages, LaTeX, references added, typos corrected, version to appear in J. Math. Phys