Feynman-Schwinger representation approach to nonperturbative physics

Journal Article · Mon Nov 01 04:00:00 EST 1999 · Physical Review, C

DOI:https://doi.org/10.1103/PhysRevC.60.055210· OSTI ID:688073

Savkli, C; Gross, F ^[1]; Tjon, J ^[2]; Gross, F ^[3]

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1. Department of Physics, College of William and Mary, Williamsburg, Virginia 23187 (United States)
2. Institute for Theoretical Physics, University of Utrecht, Princetonplein 5, P.O. Box 80.006, 3508 TA Utrecht (the Netherlands)
3. Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606 (United States)

The Feynman-Schwinger representation provides a convenient framework for the calculation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this toy model we illustrate how the formalism works. The analytic result for the self-energy is compared with the perturbative result. Next, using a {chi}{sup 2}{phi} interaction, we discuss the regularization of various divergences encountered in this formalism. The ultraviolet divergence, which is common in standard perturbative field theory applications, is removed by using a Pauli-Villars regularization. We show that the divergence associated with large values of Feynman-Schwinger parameter {ital s} is spurious and it can be avoided by using an imaginary Feynman parameter is. {copyright} {ital 1999} {ital The American Physical Society}

• Sponsoring Organization: USDOE
• OSTI ID: 688073
• Journal Information: Physical Review, C, Journal Name: Physical Review, C Journal Issue: 5 Vol. 60; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUND STATE
FEYNMAN PATH INTEGRAL
PROPAGATOR
QUANTUM ELECTRODYNAMICS
ULTRAVIOLET DIVERGENCES