Translation invariance and a reduced model for summing planar diagrams in QCD

Sumit R. Das; Spenta R. Wadia

doi:10.1016/0370-2693(82)90552-4

Translation invariance and a reduced model for summing planar diagrams in QCD

Sumit R. Das, Spenta R. Wadia

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

A reduction of degrees of freedom at large N is performed by representing space-time translations in the internal symmetry group. The reduced model for the U(∞) gauge theory is constructed in a translation invariant gauge. The rule is U(x, x+μ)→D_k(x)V_μD_k⁺(x) where V_μ belong to the coset U(N) U(1)^N and D_k(x) is a diagonal plane-wave matrix representing translations. We show that at large N, the planar perturbation expansion of the gauge theory is identical to that of the reduced model.

Original language	English
Pages (from-to)	228-232
Number of pages	5
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	117
Issue number	3-4
DOIs	https://doi.org/10.1016/0370-2693(82)90552-4
State	Published - Nov 11 1982

Bibliographical note

Funding Information:
'~ Work supported in part by the DOE: AE-AC02-81ER 10957A; and by the NSF: PHY79-23669. z Permanent address after October 1, 1982: Theoretical Phys-ics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India.

Funding

'~ Work supported in part by the DOE: AE-AC02-81ER 10957A; and by the NSF: PHY79-23669. z Permanent address after October 1, 1982: Theoretical Phys-ics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India.

Funders	Funder number
National Science Foundation (NSF)	PHY79-23669
Michigan State University-U.S. Department of Energy (MSU-DOE) Plant Research Laboratory	AE-AC02-81ER 10957A

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1016/0370-2693(82)90552-4

Cite this

@article{52f5894bb3734516ab9d468240886e17,

title = "Translation invariance and a reduced model for summing planar diagrams in QCD",

abstract = "A reduction of degrees of freedom at large N is performed by representing space-time translations in the internal symmetry group. The reduced model for the U(∞) gauge theory is constructed in a translation invariant gauge. The rule is U(x, x+μ)→Dk(x)VμDk+(x) where Vμ belong to the coset U(N) U(1)N and Dk(x) is a diagonal plane-wave matrix representing translations. We show that at large N, the planar perturbation expansion of the gauge theory is identical to that of the reduced model.",

author = "{R. Das}, Sumit and {R. Wadia}, Spenta",

note = "Funding Information: '~ Work supported in part by the DOE: AE-AC02-81ER 10957A; and by the NSF: PHY79-23669. z Permanent address after October 1, 1982: Theoretical Phys-ics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India.",

year = "1982",

month = nov,

day = "11",

doi = "10.1016/0370-2693(82)90552-4",

language = "English",

volume = "117",

pages = "228--232",

number = "3-4",

}

TY - JOUR

T1 - Translation invariance and a reduced model for summing planar diagrams in QCD

AU - R. Das, Sumit

AU - R. Wadia, Spenta

N1 - Funding Information: '~ Work supported in part by the DOE: AE-AC02-81ER 10957A; and by the NSF: PHY79-23669. z Permanent address after October 1, 1982: Theoretical Phys-ics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India.

PY - 1982/11/11

Y1 - 1982/11/11

N2 - A reduction of degrees of freedom at large N is performed by representing space-time translations in the internal symmetry group. The reduced model for the U(∞) gauge theory is constructed in a translation invariant gauge. The rule is U(x, x+μ)→Dk(x)VμDk+(x) where Vμ belong to the coset U(N) U(1)N and Dk(x) is a diagonal plane-wave matrix representing translations. We show that at large N, the planar perturbation expansion of the gauge theory is identical to that of the reduced model.

AB - A reduction of degrees of freedom at large N is performed by representing space-time translations in the internal symmetry group. The reduced model for the U(∞) gauge theory is constructed in a translation invariant gauge. The rule is U(x, x+μ)→Dk(x)VμDk+(x) where Vμ belong to the coset U(N) U(1)N and Dk(x) is a diagonal plane-wave matrix representing translations. We show that at large N, the planar perturbation expansion of the gauge theory is identical to that of the reduced model.

UR - http://www.scopus.com/inward/record.url?scp=0001636840&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001636840&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(82)90552-4

DO - 10.1016/0370-2693(82)90552-4

M3 - Article

AN - SCOPUS:0001636840

SN - 0370-2693

VL - 117

SP - 228

EP - 232

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 3-4

ER -

Translation invariance and a reduced model for summing planar diagrams in QCD

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this