delta. expansion for local gauge theories. I. A one-dimensional model

Journal Article · Sat Feb 15 04:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.1248· OSTI ID:7235258

Bender, C M ^[1]; Cooper, F ^[2]; Milton, K A ^[3]; Moshe, M ^[1]; Pinsky, S S ^[4]; Simmons, Jr, L M ^[2]

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1. Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019 (United States)
4. Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)

The principles of the {delta} perturbation theory were first proposed in the context of self-interacting scalar quantum field theory. There it was shown how to expand a ({phi}{sup 2}){sup 1+{delta}} theory as a series in powers of {delta} and how to recover nonperturbative information about a {phi}{sup 4} field theory from the {delta} expansion at {delta}=1. The purpose of this series of papers is to extend the notions of {delta} perturbation theory from boson theories to theories having a local gauge symmetry. In the case of quantum electrodynamics one introduces the parameter {delta} by generalizing the minimal coupling terms to {bar {psi}}({partial derivative}{minus}{ital ieA}){sup {delta}}{psi} and expanding in powers of {delta}. This interaction preserves local gauge invariance for all {delta}. While there are enormous benefits in using the {delta} expansion (obtaining nonperturbative results), gauge theories present new technical difficulties not encountered in self-interacting boson theories because the expression ({partial derivative}{minus}{ital ieA}){sup {delta}} contains a derivative operator. In the first paper of this series a one-dimensional model whose interaction term has the form {bar {psi}}({ital d}/{ital dt}{minus}{ital ig}{phi}({ital t})){sup {delta}}{psi} is considered. The virtue of this model is that it provides a laboratory in which to study fractional powers of derivative operators without the added complexity of {gamma} matrices. In the next paper of this series we consider two-dimensional electrodynamics and show how to calculate the anomaly in the {delta} expansion.

• OSTI ID: 7235258
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 45:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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662220* -- Quantum Electrodynamics-- (1992-)
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ELEMENTARY PARTICLES
FIELD THEORIES
FUNCTIONS
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