Quantum charged fields in Rindler space

TL;DR

This paper investigates the quantization of charged scalar fields in Rindler space under a constant electric field, deriving vacuum decay rates, connecting Minkowski and Rindler modes, and analyzing detector physics in this context.

Contribution

It provides a detailed analysis of charged field quantization in Rindler space, including vacuum decay, mode relations, and detector dynamics, extending understanding of quantum fields in accelerated frames.

Findings

Derived the Schwinger vacuum decay rate using operator and path integral formalisms.

Established algebraic relations connecting Minkowski and Rindler modes.

Showed the detector's behavior approaches thermal equilibrium in certain limits.

Abstract

We study, using Rindler coordinates, the quantization of a charged scalar field interacting with a constant, external, electric field. First we establish the expression of the Schwinger vacuum decay rate, using the operator formalism. Then we rederive it in the framework of the Feynman path integral method. Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propagator. Moreover we compute the expression of the Unruh's modes that allow to make connection between Minkowskian and Rindlerian quantization scheme by purely algebraic relations. We use these modes to study the physics of a charged two level detector moving in an electric field whose transitions are due to the exchange of charged quanta. In the limit where the Schwinger pair production mechanism of the exchanged quanta becomes negligible we recover the Boltzman equilibrium ratio for the population of the levels of the detector. Finally we explicitly show how the detector can be taken as the large mass and charge limit of an interacting fields system.