Complex Effective Path: A Semi-Classical Probe of Quantum Effects

TL;DR

This paper introduces the concept of a complex effective path derived from the quantum effective action, linking its imaginary part to particle creation phenomena, with applications including black hole radiation.

Contribution

It proposes a novel semi-classical method to analyze quantum effects via complex effective paths, extending the understanding of particle creation in curved spacetime.

Findings

Effective path encodes particle creation information.

Imaginary part of the effective action relates to black hole radiation.

Method provides new insights into quantum effects in gravitational fields.

Abstract

We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the effective path will also, in general, be complex. The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation. We try to identify such features using simple examples including that of effective path through the black hole horizon leading to thermal radiation. Implications of this approach are discussed.