Quadratic divergences in dimensional renormalization of 1/N expansions

Journal Article · Sun Dec 15 00:00:00 EST 1985 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.32.3244· OSTI ID:6197790

Rim, C; Weisberger, W I

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.

• Research Organization: Department of Physics, Chonbug National University, Chonju 520, R. O. Korea
• OSTI ID: 6197790
• Journal Information: Phys. Rev. D; (United States), Vol. 32:12
• Country of Publication: United States
• Language: English

Related Subjects

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