The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schrödinger equation in which the role of time is played by the deformation parameter ℏ and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions.
Cite this article
Alan Weinstein, Classical Theta Functions and Quantum Tori. Publ. Res. Inst. Math. Sci. 30 (1994), no. 2, pp. 327–333DOI 10.2977/PRIMS/1195166136