Dimensional renormalization in {phi}{sup 3} theory: Ladders and rainbows

Journal Article · Tue Apr 01 00:00:00 EST 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.55.5230· OSTI ID:562394

Delbourgo, R; Elliott, D ^[1]; McAnally, D S ^[2]

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1. University of Tasmania, GPO Box 252-21, Hobart, Tasmania 7001 (Australia)
2. University of Queensland, St Lucia, Brisbane, Queensland 4067 (Australia)

The sum of all the ladder and rainbow diagrams in {phi}{sup 3} theory near six dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hypergeometric functions; the expansion and representation of these functions can then be used to prove the absence of renormalization factors which are transcendental for this theory and this topology to all orders in perturbation theory. The correct anomalous scaling dimensions of the Green functions are also obtained in the six-dimensional limit. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 562394
• Journal Information: Physical Review, D, Vol. 55, Issue 8; Other Information: PBD: Apr 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
SCALAR FIELDS
QUANTUM FIELD THEORY
RENORMALIZATION
AXIOMATIC FIELD THEORY
DIFFERENTIAL EQUATIONS
TOPOLOGY
PERTURBATION THEORY
GREEN FUNCTION
MANY-DIMENSIONAL CALCULATIONS
SCALING LAWS
SERIES EXPANSION
NONLINEAR PROBLEMS
FEYNMAN DIAGRAM