Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

Abstract

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, produce significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.

25 pags, 19 figures, prepared for the volume celebrating the 70th birthday of Yuri Simonov

References in corpus (5)

• The Feynman-Schwinger representation in QCD
• The stability of the scalar ${\chi }^2\varphi$ interaction
• Baryon magnetic moments in the effective quark Lagrangian approach
• The role of interaction vertices in bound state calculations
• The Feynman-Schwinger (world-line) representation in perturbative QCD

Cited by in corpus (13)

• Quantum effective actions from nonperturbative worldline dynamics
• Manifestation of three-body forces in three-body Bethe-Salpeter and light-front equations
• 3-point off-shell vertex in scalar QED in arbitrary gauge and dimension
• Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space
• Propagator from Nonperturbative Worldline Dynamics
• Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
• Integral representations combining ladders and crossed-ladders
• Asymptotic behavior and critical coupling in the scalar Yukawa model from Schwinger-Dyson equations
• Light-Front Dynamic Analysis of Bound States in Scalar Field Model
• Color-suppression of non-planar diagrams in bosonic bound states
• Applications of the worldline Monte Carlo formalism in quantum mechanics
• On the phase structure of vector-matrix scalar model in four dimensions
• Removal of singularities from the covariant spectator theory