Geometry of spin-field coupling on the worldline

Abstract

We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the loop-space approach to gauge theory. In particular, we employ the loop (or area) derivative operator on the space of all holonomies which can immediately be applied to the worldline representation of the effective action. This results in a spin factor that associates the information about spin with "zigzag" motion of the fluctuating field. Concentrating on the case of quantum electrodynamics in external fields, we obtain a purely geometric representation of the Pauli term. To one-loop order, we confirm our formalism by rederiving the Heisenberg-Euler effective action. Furthermore, we give closed-form worldline representations for the all-loop order effective action to lowest nontrivial order in a small-N_f expansion.

18 pages, v2: references added, minor changes, matches PRD version

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Cited by in corpus (7)

• Discrete worldline instantons
• Quantum effective actions from nonperturbative worldline dynamics
• Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering
• Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields
• The QED four -- photon amplitudes off-shell: part 1
• The QED four-photon amplitudes off-shell: part 2
• Spin in the Worldline Path Integral in 2+1 Dimensions