Truncating the Schwinger-Dyson equations: How multiplicative renormalizability and the Ward identity restrict the three-point vertex in QED

Journal Article · Sat Dec 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.4165· OSTI ID:5828519

Curtis, D C; Pennington, M R ^[1]

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1. Centre for Particle Theory, University of Durham, Durham (United Kingdom)

Nonperturbative studies of field theory require the Schwinger-Dyson equations to be truncated to make them tractable. Thus, when investigating the behavior of the fermion propagator, for example, an {ital Ansatz} for the three-point vertex has to be made. While the well-known Ward identity determines the longitudinal part of this vertex in terms of the fermion propagator as shown by Ball and Chiu, it leaves the transverse part unconstrained. However, Brown and Dorey have recently emphasized that the requirement of multiplicative renormalizability is not satisfied by arbitrary {ital Ansatz} for the vertex. We show how this requirement restricts the form of the transverse part. By considering the example of QED in the quenched approximation, we present a form for the vertex that not only satisfies the Ward identity but is multiplicatively renormalizable to all orders in leading and next-to-leading logarithms in perturbation theory and so provides a suitable {ital Ansatz} for the full three-point vertex.

• OSTI ID: 5828519
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:12; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645000* -- High Energy Physics
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON EXPANSION
DYSON REPRESENTATION
ELECTRODYNAMICS
FERMIONS
FIELD THEORIES
PERTURBATION THEORY
PROPAGATOR
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
WARD IDENTITY