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Title: Quadratic divergences in dimensional renormalization of 1/N expansions

Abstract

We calculate the ultraviolet divergences of the scalar O(N) model in the 1/N expansion near four dimensions (d = 4-epsilon). At next to leading order in (1/N) the point d = 4 becomes an essential singularity as the accumulation point of an infinite sequence of poles at epsilon = 2/k for integer k. Such singular behavior renders the dimensionally renormalized interacting theory unsummable. These singularities are not predicted when the perturbatively calculated renormalization constants are reexpanded in powers of 1/N. Rather they arise from the summation of the infinite subset of quadratically divergent Feynman diagrams which make up each order of the 1/N expansion. Such pathological behavior should be a general feature of dimensional renormalization when quadratic divergences are treated nonperturbatively.

Authors:
;
Publication Date:
Research Org.:
Department of Physics, Chonbug National University, Chonju 520, R. O. Korea
OSTI Identifier:
6197790
Resource Type:
Journal Article
Journal Name:
Phys. Rev. D; (United States)
Additional Journal Information:
Journal Volume: 32:12
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCALAR FIELDS; RENORMALIZATION; ULTRAVIOLET DIVERGENCES; FEYNMAN DIAGRAM; O GROUPS; PERTURBATION THEORY; SELF-ENERGY; SPACE-TIME; WAVE FUNCTIONS; DIAGRAMS; DYNAMICAL GROUPS; ENERGY; FUNCTIONS; LIE GROUPS; SYMMETRY GROUPS; 645400* - High Energy Physics- Field Theory

Citation Formats

Rim, C, and Weisberger, W I. Quadratic divergences in dimensional renormalization of 1/N expansions. United States: N. p., 1985. Web. doi:10.1103/PhysRevD.32.3244.
Rim, C, & Weisberger, W I. Quadratic divergences in dimensional renormalization of 1/N expansions. United States. https://doi.org/10.1103/PhysRevD.32.3244
Rim, C, and Weisberger, W I. 1985. "Quadratic divergences in dimensional renormalization of 1/N expansions". United States. https://doi.org/10.1103/PhysRevD.32.3244.
@article{osti_6197790,
title = {Quadratic divergences in dimensional renormalization of 1/N expansions},
author = {Rim, C and Weisberger, W I},
abstractNote = {We calculate the ultraviolet divergences of the scalar O(N) model in the 1/N expansion near four dimensions (d = 4-epsilon). At next to leading order in (1/N) the point d = 4 becomes an essential singularity as the accumulation point of an infinite sequence of poles at epsilon = 2/k for integer k. Such singular behavior renders the dimensionally renormalized interacting theory unsummable. These singularities are not predicted when the perturbatively calculated renormalization constants are reexpanded in powers of 1/N. Rather they arise from the summation of the infinite subset of quadratically divergent Feynman diagrams which make up each order of the 1/N expansion. Such pathological behavior should be a general feature of dimensional renormalization when quadratic divergences are treated nonperturbatively.},
doi = {10.1103/PhysRevD.32.3244},
url = {https://www.osti.gov/biblio/6197790}, journal = {Phys. Rev. D; (United States)},
number = ,
volume = 32:12,
place = {United States},
year = {Sun Dec 15 00:00:00 EST 1985},
month = {Sun Dec 15 00:00:00 EST 1985}
}