Continuum Behaviour of Lattice QED, Discretized with One-Sided Lattice Differences, in One-Loop Order

A lattice action for QED is considered, where the derivatives in the Dirac operator are replaced by one-sided lattice differences. A systematic expansion in the lattice spacing of the one-loop contribution to the fermion self energy, vacuum polarization tensor and vertex function is carried out for...

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Bibliographic Details
Published in:arXiv.org 1996-11
Main Authors: Sadooghi, Neda, Rothe, Heinz J
Format: Article
Language:English
Subjects:
Discretization
Fermions
Field theory
Mathematical analysis
Polarization
Tensors
Online Access:Get full text
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Summary:A lattice action for QED is considered, where the derivatives in the Dirac operator are replaced by one-sided lattice differences. A systematic expansion in the lattice spacing of the one-loop contribution to the fermion self energy, vacuum polarization tensor and vertex function is carried out for an arbitrary choice of one-sided lattice differences. It is shown that only the vacuum polarization tensor possesses the correct continuum limit, while the fermion self energy and vertex function receive non-covariant contributions. A lattice action, discretized with a fixed choice of one-sided lattice differences therefore does not define a renormalizable field theory. The non-covariant contributions can however be eliminated by averaging the expressions over all possible choices of one-sided lattice differences.
ISSN:2331-8422
DOI:10.48550/arxiv.9610001