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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2016, Vol. 11 Issue (6): 110310   https://doi.org/10.1007/s11467-016-0585-2
  本期目录
The combinatorics of Green’s functions in planar field theories
Kurusch Ebrahimi-Fard1,*(),Frédéric Patras2,*()
1. ICMAT, C/Nicolás Cabrera, no. 13-15, 28049 Madrid, Spain. On leave from UHA, Mulhouse, France
2. Univ. de Nice, Labo. J.-A. Dieudonné, UMR 7351, CNRS, Parc Valrose, 06108 Nice Cedex 02, France
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Abstract

The aim of this exposition is to provide a detailed description of the use of combinatorial algebra in quantum field theory in the planar setting. Particular emphasis is placed on the relations between different types of planar Green’s functions. The primary object is a Hopf algebra that is naturally defined on variables representing non-commuting sources, and whose coproduct splits into two halfcoproducts. The latter give rise to the notion of an unshuffle bialgebra. This setting allows a description of the relation between full and connected planar Green’s functions to be given by solving a simple linear fixed point equation. We also include a brief outline of the consequences of our approach in the framework of ordinary quantum field theory.

Key wordsplanar field theory    Green’s functions    free probability    Hopf algebra    shuffle algebra    partitions
收稿日期: 2015-10-22      出版日期: 2016-08-16
Corresponding Author(s): Kurusch Ebrahimi-Fard,Frédéric Patras   
 引用本文:   
. [J]. Frontiers of Physics, 2016, 11(6): 110310.
Kurusch Ebrahimi-Fard,Frédéric Patras. The combinatorics of Green’s functions in planar field theories. Front. Phys. , 2016, 11(6): 110310.
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https://academic.hep.com.cn/fop/CN/10.1007/s11467-016-0585-2
https://academic.hep.com.cn/fop/CN/Y2016/V11/I6/110310
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