The Feynman Variational Principle in the Worldline Representation of Field Theory

Details The Feynman Variational Principle in the Worldline Representation of Field Theory The Feynman Variational Principle in the Worldline Representation of Field Theory

1998-10-28

arxiv.org/abs/hep-th/9810232v1

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, revtex, no figures. To appear in Proceedings of PI98, Florence, Italy

Scientific paper

Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in terms of particle trajectories (worldlines) instead of field operators. The Green functions of the theory are then approximated variationally on the pole of the external particles by using a retarded quadratic trial action. Application to a scalar theory gives non-perturbative, covariant results for vertex functions and scattering processes. Recent progress in dealing with the spin degrees of freedom in fermionic systems, in particular Quantum Electrodynamics, is discussed. We evaluate the averages needed in the Feynman variational principle for a general quadratic trial action and study the structure of the dressed fermion propagator.

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