Infrared problem vs gauge choice: scattering of classical Dirac field

Abstract

We consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $F=F^{\mathrm{ret}}+F^{\mathrm{in}}=F^{\mathrm{adv}}+F^{\mathrm{out}}$, where the current producing $F^{\mathrm{ret}/\mathrm{adv}}$ has past and future asymptotes homogeneous of degree $-3$, and the free fields $F^{\mathrm{in}/\mathrm{out}}$ are radiation fields produced by currents with similar asymptotic behavior. We show the existence of the electromagnetic gauges in which the particle has 'in' and 'out' asymptotic states approaching free field states, with no long-time corrections of the free dynamics. Using a special Cauchy foliation of the spacetime we show in this context the existence and asymptotic completeness of the wave operators. Moreover, we define a special 'evolution picture' in which the free evolution operator has well-defined limits for $t\to \pm \infty$, thus the scattering wave operators do not need the free evolution counteraction.

arXiv comment57 pages

References in corpus (7)

• Wave Equations on Lorentzian Manifolds and Quantization
• Asymptotic structure of electrodynamics revisited
• From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons
• Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics
• Asymptotic charges, large gauge transformations and inequivalence of different gauges in external current QED
• Asymptotic completeness, global existence and the infrared problem for the Maxwell-Dirac equations
• Electromagnetic gauge choice for scattering of Schrödinger particle

Cited by in corpus (1)

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