Hamilton-Jacobi Method and Gravitation

TL;DR

This paper demonstrates how the Hamilton-Jacobi semi-classical method can be used to extract quantitative predictions about quantum fields in curved spacetime, aligning well with exact quantum field theory results in symmetric cases.

Contribution

It shows the effectiveness of the Hamilton-Jacobi method in deriving accurate physical predictions in curved spacetime scenarios, bridging semi-classical and quantum results.

Findings

Hamilton-Jacobi method agrees with quantum field theory in symmetric cases

Semi-classical approach provides reliable predictions in curved spacetime

Method applicable to a variety of physical phenomena

Abstract

Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations.