Higher Order Corrections to the Asymptotic Perturbative Solution of a Schwinger-Dyson Equation

被引：12

作者：

Bellon, Marc P. ^{[1
,2
]}

Clavier, Pierre J. ^{[1
,2
]}

机构：

[1] Univ Paris 06, Sorbonne Univ, LPTHE, UMR 7589, F-75005 Paris, France

[2] CNRS, UMR 7589, LPTHE, F-75005 Paris, France

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2014年 / 104卷 / 06期

关键词：

renormalisation; Schwinger-Dyson equation; Borel transformation; QUANTUM-FIELD THEORY; RENORMALIZATION-GROUP; HOPF-ALGEBRAS;

D O I：

10.1007/s11005-014-0686-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Building on our previous works on perturbative solutions to a Schwinger-Dyson for the massless Wess-Zumino model, we show how to compute 1/n corrections to its asymptotic behavior. The coefficients are analytically determined through a sum on all the poles of the Mellin transform of the one-loop diagram. We present results up to the fourth order in 1/n as well as a comparison with numerical results. Unexpected cancellations of zetas are observed in the solution, so that no even zetas appear and the weight of the coefficients is lower than expected, which suggests the existence of more structure in the theory.

引用

页码：749 / 770

页数：22

共 12 条

[1]

Adnan B., 2012, COMMUN THEOR PHYS, V58, P79, DOI [10.1088/0253-6102/58/1/16, DOI 10.1088/0253-6102/58/1/16]

[2]

[Anonymous], 1964, APPL MATH SERIES

[3] Renormalization group functions for the Wess-Zumino model: Up to 200 loops through Hopf algebras [J].

Bellon, Marc P. ;

Schaposnik, Fidel A. .

NUCLEAR PHYSICS B, 2008, 800 (03) :517-526

[4] Higher Loop Corrections to a Schwinger-Dyson Equation [J].

Bellon, Marc P. ;

Schaposnik, Fidel A. .

LETTERS IN MATHEMATICAL PHYSICS, 2013, 103 (08) :881-893

[5] An Efficient Method for the Solution of Schwinger-Dyson Equations for Propagators [J].

Bellon, Marc P. .

LETTERS IN MATHEMATICAL PHYSICS, 2010, 94 (01) :77-86

[6] Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality [J].

Broadhurst, DJ ;

Kreimer, D .

NUCLEAR PHYSICS B, 2001, 600 (02) :403-422

[7] Renormalization in quantum field theory and the Riemann-Hilbert problem II:: The β-function, diffeomorphisms and the renormalization group [J].

Connes, A ;

Kreimer, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 216 (01) :215-241

[8] Renormalization in quantum field theory and the Riemann-Hilbert problem I: The Hopf algebra structure of graphs and the main theorem [J].

Connes, A ;

Kreimer, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 210 (01) :249-273

[9] An etude in non-linear Dyson-Schwinger equations [J].

Kreimer, Dirk ;

Yeats, Karen .

NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS, 2006, 160 :116-121

[10]

Piguet O, 1986, RENORMALIZED SUPERSY

← 1 2 →