Quantum charged fields in (1+1) Rindler space

We study, using Rindler coordinates, the quantization of a charged scalar h eld interacting with a constant (Poincare invariant), external, electric fi eld in (1+1) dimensionnal flatspace: our main motivation is pedagogy. We il lustrate in this framework the equivalence between various approaches to fi eld quantization commonly used in the framework of curved backgrounds. Firs t we establish the expression of the Schwinger vacuum decay rate, using the operator formalism. Then we rederive it in the framework of the Feynman pa th integral method. Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propa gator. Moreover, we compute the expression of the Unruh's modes that allow us to make a connection between the Minkowskian and Rindlerian quantization schemes by purely algebraic relations. We use these modes to study the phy sics of a charged two level detector moving in an electric field whose tran sitions are due to the exchange of charged quanta. In the limit where the S chwinger pair production mechanism of the exchanged quanta becomes negligib le we recover the Boltzman equilibrium ratio for the population of the leve ls of the detector. Finally we explicitly show how the detector can be take n as the large mass and charge limit of an interacting fields system. (C) 2 000 Academic Press.