Semiclassical Scalar Pair Production in a Circularly Polarized Electric Field: Analytic Consistency and Momentum Dependence

Abstract

We present a detailed semiclassical analysis of vacuum pair production of charged scalar particles in a spatially homogeneous, circularly polarized electric field. Starting from the Klein–Gordon equation, we derive the mode equation and evaluate the tunneling exponent governing pair creation using a WKB approach in the adiabatic regime. The imaginary part of the semiclassical action is obtained in closed analytic form and shown to reduce smoothly to the standard Schwinger result in the low-frequency limit, independent of polarization geometry. We analyze the transverse momentum dependence of the tunneling probability and demonstrate that the dominant contribution arises from small transverse momenta, as in constant and linearly polarized fields. The corresponding pair-production rate reproduces the leading-order scalar Schwinger formula, providing a nontrivial consistency check of the formalism. The results clarify how circular polarization enters intermediate steps of the semiclassical calculation while canceling from the leading tunneling exponent, and they provide a transparent analytic benchmark for semiclassical treatments of rotating background fields.