Area Potentials and Deformation Quantization

TL;DR

This paper explores N-body systems with interactions beyond pairs, analyzing their classical and quantum behavior in phase space through Wigner functions, providing insights into their deformation quantization.

Contribution

It introduces a formulation for N-body interactions on the plane and analyzes their Wigner functions in phase-space quantization, extending beyond traditional 2-body systems.

Findings

Wigner functions for complex N-body systems are derived.

Classical and quantum behaviors are compared in phase space.

New insights into deformation quantization for multi-body systems.

Abstract

Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions--the density matrices in phase-space quantization--are given and analyzed.