Decoherence of Correlation Histories

Summary

Abstract

We use a λΦ⁴ scalar quantum field theory to illustrate a new approach to the study of quantum to classical transition. In this approach, the decoherence functional is employed to assign probabilities to consistent histories defined in terms of correlations among the fields at separate points, rather than the field itself. We present expressions for the quantum amplitudes associated with such histories, as well as for the decoherence functional between two of them. The dynamics of an individual consistent history may be described by a Langevintype equation, which we derive.

Dedicated to Professor Brill on the occasion of his sixtieth birthday, August 1993

Introduction

Interpretations of Quantum Mechanics and Paradigms of Statistical Mechanics

This paper attempts to bring together two basic concepts, one from the foundations of statistical mechanics and the other from the foundations of quantum mechanics, for the purpose of addressing two basic issues in physics:

1. the quantum to classical transition, and

2. the quantum origin of stochastic dynamics.

Both issues draw in the interlaced effects of dissipation, decoherence, noise, and fluctuation. A central concern is the role played by coarse-graining —the naturalness of its choice, the effectiveness of its implementation and the relevance of its consequences.