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. 327–333