First Order Variational Calculation of Form Factor in a Scalar Nucleon--Meson Theory

Abstract

We investigate a relativistic quantum field theory in the particle representation using a non-perturbative variational technique. The theory is that of two massive scalar particles, `nucleons' and `mesons', interacting via a Yukawa coupling. We calculate the general Euclidean Green function involving two external nucleons and an arbitrary number of external mesons in the quenched approximation for the nucleons. The non-perturbative renormalization and truncation is done in a consistent manner and results in the same variational functional independent of the number of external mesons. We check that the calculation agrees with one-loop perturbation theory for small couplings. As an illustration the special case of meson absorption on the nucleon is considered in detail. We derive the radius of the dressed particle and numerically investigate the vertex function after analytic continuation to Minkowski space.

28 pages standard LaTeX, 13 uuencoded postscript figures embedded with psfig.sty

References in corpus (3)

• Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism
• Polaron Variational Methods In The Particle Representation Of Field Theory : II. Numerical Results For The Propagator
• Bound state solutions of scalar QED_{2+1} for zero photon mass

Cited by in corpus (6)

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• Variational Field Theoretic Approach to Relativistic Scattering
• Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem
• On the Numerical Evaluation of a Class of Oscillatory Integrals in Worldline Variational Calculations