skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nonperturbative renormalization of scalar quantum electrodynamics in d=3

Abstract

For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban’s approach to the renormalization group.

Authors:
 [1]
  1. Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260 (United States)
Publication Date:
OSTI Identifier:
22479544
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; PERTURBATION THEORY; QUANTUM ELECTRODYNAMICS; RENORMALIZATION

Citation Formats

Dimock, J., E-mail: dimock@buffalo.edu. Nonperturbative renormalization of scalar quantum electrodynamics in d=3. United States: N. p., 2015. Web. doi:10.1063/1.4933224.
Dimock, J., E-mail: dimock@buffalo.edu. Nonperturbative renormalization of scalar quantum electrodynamics in d=3. United States. https://doi.org/10.1063/1.4933224
Dimock, J., E-mail: dimock@buffalo.edu. 2015. "Nonperturbative renormalization of scalar quantum electrodynamics in d=3". United States. https://doi.org/10.1063/1.4933224.
@article{osti_22479544,
title = {Nonperturbative renormalization of scalar quantum electrodynamics in d=3},
author = {Dimock, J., E-mail: dimock@buffalo.edu},
abstractNote = {For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban’s approach to the renormalization group.},
doi = {10.1063/1.4933224},
url = {https://www.osti.gov/biblio/22479544}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 10,
volume = 56,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2015},
month = {Thu Oct 15 00:00:00 EDT 2015}
}