The weak-field expansion for processes in a homogeneous background magnetic field

Abstract

The weak-field expansion of the charged fermion propagator under a uniform magnetic field is studied. Starting from Schwinger's proper-time representation, we express the charged fermion propagator as an infinite series corresponding to different Landau levels. This infinite series is then reorganized according to the powers of the external field strength $B$. For illustration, we apply this expansion to $\gamma \to \nu \bar{\nu }$ and $\nu \to \nu \gamma$ decays, which involve charged fermions in the internal loop. The leading and subleading magnetic-field effects to the above processes are computed.

17 pages, section IIIB added, some typos corrected

References in corpus (6)

• Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations
• Photon Splitting in a Very Strong Magnetic Field
• Cherenkov radiation by massless neutrinos in a magnetic field
• Photon-neutrino interactions
• gamma nu -> gamma gamma nu and crossed processes at energies below m_W
• Neutrino-photon scattering and its crossed processes in a background magnetic field

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