Random walks of partons in SU(N{sub c}) and classical representations of color charges in QCD at small x

Journal Article · Mon Nov 15 00:00:00 EST 2004 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.70.105012· OSTI ID:20698043

Jeon, Sangyong; Venugopalan, Raju ^[1]

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1. Physics Department, McGill University, Montreal, QC H3A-2T8 (Canada)

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N{sub c}) color group. The problem can be formulated as a random walk of partons in the N{sub c}-1 dimensional space of the Casimir operators of SU(N{sub c}). For a large number of sources, k>>1, we show explicitly that the most likely representation is a classical representation of order O({radical}(k)). The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher N{sub c}-2 Casimir operators are suppressed by powers of k. Other applications of the techniques developed here are discussed briefly.

• OSTI ID: 20698043
• Journal Information: Physical Review. D, Particles Fields, Vol. 70, Issue 10; Other Information: DOI: 10.1103/PhysRevD.70.105012; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
CASIMIR EFFECT
CASIMIR OPERATORS
HEAVY NUCLEI
LATTICE FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
PARTON MODEL
PARTONS
PATH INTEGRALS
QUANTUM CHROMODYNAMICS
RANDOMNESS
SU-2 GROUPS
SU-3 GROUPS
SU-4 GROUPS
SU-5 GROUPS
SU-6 GROUPS
SU-7 GROUPS
SU-8 GROUPS