On the Passage from the Quantum theory to the Semi-Classical theory

TL;DR

This paper explores the transition from quantum to semi-classical descriptions in the CGHS model, highlighting the importance of correlations, and proposing a coherent state approach that may involve spontaneous symmetry breaking.

Contribution

It introduces a coherent state formalism for semi-classical analysis in dilaton gravity, addressing limitations of traditional constraint quantization methods.

Findings

Correlations cannot be ignored at Hawking-effect accuracy levels.

Standard constraint procedures obscure semi-classical physics.

Coherent states provide a consistent semi-classical framework.

Abstract

In this paper an attempt is made to understand the passage from the exact quantum treatment of the CGHS theory to the semi-classical physics discussed by many authors. We find first that to the order of accuracy to which Hawking effects are calculated in the theory, it is inconsistent to ignore correlations in the dilaton gravity sector. Next the standard Dirac or BRST procedure for implementing the constraints is followed. This leads to a set of physical states, in which however the semi-classical physics of the theory seems to be completely obscured. As an alternative, we construct a coherent state formalism, which is the natural framework for understanding the semi-classical calculations, and argue that it satisfies all necessary requirements of the theory, provided that there exist classical ghost configurations which solve an infinite set of equations. If this is the case it may be interpreted as a spontaneous breakdown of general covariance.