Geometry of spin-field coupling on the worldline

Details Geometry of spin-field coupling on the worldline Geometry of spin-field coupling on the worldline

2005-05-09

arxiv.org/abs/hep-th/0505072v2

Phys.Rev. D72 (2005) 065018

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.72.065018

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.

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