QED vacuum polarization on a momentum lattice

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

DOI:https://doi.org/10.1103/PhysRevD.46.5540· OSTI ID:6892920

Kroeger, H; Lafrance, R; Marleau, L ^[1]

---

1. Departement de Physique, Universite Laval, Quebec, Quebec, G1K7P4 (Canada)

We study the effect of a momentum ([ital k]) lattice as a regulator of quantum field theory. An an example, we compute the vacuum polarization in noncompact (linearized) QED from [ital k]-lattice perturbation theory to one-loop order and study the continuum limit. The amplitude has a finite part plus logarithmically, linearly, and quadratically divergent terms. The amplitude violates gauge invariance (Ward identity) and Lorentz (Euclidean) invariance and is nonlocal. For example, the linear term [similar to][Lambda][vert bar][ital k][vert bar] is nonlocal. Renormalization requires nonlocal counterterms, which is not inconsistent because the original action on the [ital k] lattice already has a nonlocality. We explicitly give the counterterms, which render the amplitude Lorentz and gauge invariant to recover the standard result.

• OSTI ID: 6892920
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
ELECTRODYNAMICS
EQUATIONS
EQUATIONS OF STATE
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
LORENTZ INVARIANCE
PERTURBATION THEORY
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
SPACE-TIME
VACUUM POLARIZATION
WARD IDENTITY