Intrinsic quantum dynamics and its operator representation over a plane with a nonstandard connection. (English) Zbl 1105.81304

Grigor’ev, O. N.; Karasev, M. V.

Russ. J. Math. Phys. 10, No. 4, 422-435 (2003).

Summary: Using an intrinsic dynamical Schrödinger-type equation, exact associative noncommutative products of functions over a plane with nonstandard connection are constructed. For one of these products, an operator representation is found. The left regular representation of the generators of the algebra is evaluated, and the weak asymptotics of the quantum products in the sense of the theory of deformation quantization is presented.

MSC:

81S10	Geometry and quantization, symplectic methods
53D55	Deformation quantization, star products
81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory