Sharp values for all dynamical variables via Anti-Wick quantization

TL;DR

This paper introduces an approach using Anti-Wick quantization to interpret quantum expectation values as phase-space averages, providing a classical-like probabilistic framework that may help address the quantum measurement problem.

Contribution

It demonstrates that Anti-Wick quantization allows quantum expectation values to be viewed as weighted phase-space averages, bridging classical and quantum interpretations.

Findings

Quantum expectation values can be interpreted as phase-space averages.

The Husimi Q-function acts as a true probability density in phase space.

This approach retains the operator correspondence while enabling a classical-like interpretation.

Abstract

This paper proposes an approach to interpreting quantum expectation values that may help address the quantum measurement problem. Quantum expectation values are usually calculated via Hilbert space inner products and, thereby, differently from expectation values in classical mechanics, which are weighted phase-space integrals. It is shown that, by using Anti-Wick quantization to associate dynamical variables with self-adjoint linear operators, quantum expectation values can be interpreted as genuine weighted averages over phase space, paralleling their classical counterparts. This interpretation arises naturally in the Segal-Bargmann space, where creation and annihilation operators act as simple multiplication and differentiation operators. In this setting, the Husimi Q-function - the coherent-state representation of the quantum state - can be seen as a true probability density in phase space. Unlike Bohmian mechanics, the present approach retains the standard correspondence between dynamical variables and self-adjoint operators while paving the way for a classical-like probabilistic interpretation of quantum statistics.