On Geometry of p-Adic Coherent States and Mutually Unbiased Bases

This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators.

Automated summary

This paper investigates the representation of Weyl commutation relations using coherent states over a field of p-adic numbers. A lattice in a vector space over the p-adic field corresponds to a family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and the operators defining the quantization of symplectic dynamics are Hadamard operators.