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Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED

Technical Report:

Abstract

We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik {beta} function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action  More>>
Authors:
Goeckeler, M; Horsley, R; [1]  Rakow, P; [2]  Schierholz, G; [3]  Sommer, R [4] 
  1. Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Physik
  2. Freie Univ. Berlin (Germany). Inst. fuer Theoretische Physik
  3. Hoechstleistungsrechenzentrum (HLRZ), Juelich (Germany). Gruppe Theorie der Elementarteilchen
  4. European Organization for Nuclear Research, Geneva (Switzerland)
Publication Date:
Sep 01, 1991
Product Type:
Technical Report
Report Number:
DESY-91-098; HLRZ-91-71; FUB-HEP-91-9
Reference Number:
SCA: 662220; PA: DEN-92:000564; SN: 92000645443
Resource Relation:
Other Information: PBD: Sep 1991
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LATTICE FIELD THEORY; ULTRAVIOLET DIVERGENCES; UNIFIED GAUGE MODELS; QUANTUM ELECTRODYNAMICS; FERMIONS; SCALING LAWS; ASYMPTOTIC SOLUTIONS; FLUCTUATIONS; U-1 GROUPS; COUPLING CONSTANTS; SOMMERFELD CONSTANT; CHIRALITY; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; CHIRAL SYMMETRY; SYMMETRY BREAKING; BAG MODEL; ANALYTIC FUNCTIONS; CHARGE RENORMALIZATION; PERTURBATION THEORY; REST MASS; BOUND STATE; MEAN-FIELD THEORY; CORRECTIONS; CENTRAL POTENTIAL; PROPAGATOR; BOSE-EINSTEIN CONDENSATION; MASS RENORMALIZATION; PHOTONS; EXPECTATION VALUE; GOLDSTONE BOSONS; VECTOR FIELDS; 662220
OSTI ID:
10114378
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Other: ON: DE92759145; TRN: DE9200564
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
86 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Goeckeler, M, Horsley, R, Rakow, P, Schierholz, G, and Sommer, R. Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED. Germany: N. p., 1991. Web.
Goeckeler, M, Horsley, R, Rakow, P, Schierholz, G, & Sommer, R. Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED. Germany.
Goeckeler, M, Horsley, R, Rakow, P, Schierholz, G, and Sommer, R. 1991. "Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED." Germany.
@misc{etde_10114378,
title = {Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED}
author = {Goeckeler, M, Horsley, R, Rakow, P, Schierholz, G, and Sommer, R}
abstractNote = {We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik {beta} function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for small renormalized charges. (orig.).}
place = {Germany}
year = {1991}
month = {Sep}
}