Generalized quantum Vlasov equation for particle creation and unitary dynamics

Abstract

The loss of time-translational invariance caused by a time-dependent external agent leads to particle creation effects in quantum field theory. This phenomenon results in ambiguities when selecting the quantum vacuum of the canonical quantization. In this work we analyze how the time evolution of the number of created particles depends on these ambiguities when external agents are spatially homogeneous. In particular, we generalize the standard quantum Vlasov equation in order to accommodate in its formulation the possibility of having different choices of vacuum, including adiabatic vacua. This study leads us to propose a new physical criterion stronger than the unitary implementation of the dynamics in order to reduce the quantization ambiguities.

Generalized Gelfand-Dikii equation and solitonic electric fields for fermionic Schwinger pair production

“…k | 2 like in the scalar case (we choose the upper spin component for definiteness) and combining (23) and (25), one arrives at the following fermionic generalization of the Gelfand-Dikii equation ( 12…”

“…hopefully would allow one to link our fermionic generalizations of the Gelfand-Dikii equation and of the solitonic fields in a way similar to what had emerged in [27] for the scalar case. In this appendix, for completeness we review how to solve the scalar and spinor QED mode equations ( 9) and (23) for the Sauter and solitonic fields. The subscript k is omitted throughout.…”

“…At intermediate times, N k (t) is inherently ambiguous on account of its dependence on the choice of an instantaneous adiabatic basis [21,22]. Its physical meaning is presently still under discussion [20][21][22][23][24][25][26].…”