Novel perturbative scheme in quantum field theory

Carl M. Bender, Kimball A. Milton, Moshe Moshe, Stephen S. Pinsky, and L. M. Simmons, Jr.
Phys. Rev. D 37, 1472 – Published 15 March 1988
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Abstract

A novel perturbative technique for solving quantum field theory is proposed. In this paper we explore this scheme in the context of self-interacting scalar field theory. For a φ2p theory the method consists of expanding a φ2(1+δ) theory in powers of δ. A diagrammatic procedure for computing the terms in this series is given. We believe that for any Green’s function the radius of convergence of this series is finite and is, in fact, 1. Moreover, while the terms in the unrenormalized series are individually divergent, they are considerably less so than in the standard weak-coupling perturbation series. In simple, low-dimensional quantum-field-theory models, the δ expansion gives excellent numerical results. We hope this new technique will ultimately shed some light on the question of whether a (φ4)4 theory is free.

  • Received 2 November 1987

DOI:https://doi.org/10.1103/PhysRevD.37.1472

©1988 American Physical Society

Authors & Affiliations

Carl M. Bender

  • Department of Physics, Washington University, St. Louis, Missouri 63130

Kimball A. Milton

  • Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019

Moshe Moshe

  • Physics Department, Technion, Haifa 3200, Israel

Stephen S. Pinsky

  • Department of Physics, The Ohio State University, Columbus, Ohio 43210

L. M. Simmons, Jr.

  • Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

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Issue

Vol. 37, Iss. 6 — 15 March 1988

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