A soft-photon theorem for the Maxwell-Lorentz system

Dybalski, Wojciech und Duc Viet, Hoang (2019): A soft-photon theorem for the Maxwell-Lorentz system. In: Journal of Mathematical Physics, Bd. 60, Nr. 10, 102903

Abstract

For the coupled system of classical Maxwell-Lorentz equations, we show that F((x) over cap, t) = lim(vertical bar x vertical bar ->infinity)vertical bar x vertical bar F-2(x, t) and F((k) over cap, t) = lim(vertical bar k vertical bar -> 0)vertical bar k vertical bar(F) over cap (k, t), where F is the Faraday tensor, (F) over cap is its Fourier transform in space, and (x) over cap:= x/vertical bar x vertical bar, is independent of t. We combine this observation with the scattering theory for the Maxwell-Lorentz system due to Komech and Spohn, which gives the asymptotic decoupling of F into the scattered radiation F-sc,F-+/- and the soliton field F-v +/-infinity depending on the asymptotic velocity v +/-infinity of the electron at large positive (+), respectively, negative (-) times. This gives a soft photon theorem of the form F-sc,F-+((k) over cap) - F-sc,F--((k) over cap) = -(Fv+infinity((k) over cap) - Fv-infinity((k) over cap)), and analogously for F, which links the low frequency part of the scattered radiation to the change of the electron's velocity. Implications for the infrared problem in QED are discussed in the Conclusions. Published under license by AIP Publishing.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 0022-2488
• Sprache: Englisch