# Applied Mathematics to Control, Systems and Signals Research Group

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from March 30, 2009
Q-Math Seminar

# Q-Math Seminar - Season 2015/2016

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# Kurusch Ebrahimi-Fard (ICMAT)Title: On the combinatorics of planar Green's functions (I)Abstract:The aim of this series of two talks is to outline the use of combinatorial algebra in planar quantum field theory. Particular emphasis is given to the relations between the different types of planar Green’s functions. The key object is the natural Hopf algebra of non-commuting sources, and the fact that its genuine unshuffle coproduct splits into left- and right unshuffle half-coproduts. The latter give rise to the notion of unshuffle bialgebra. This setting allows to describe the relation between planar full and connected Green’s functions by solving a simple linear fixed point equation. A modification of this linear fixed point equation gives rise to the relation between connected and one-particle irreducible Green’s functions. The graphical calculus that arises from this approach also leads to a new understanding of functional calculus in planar QFT, whose rules for differentiation with respect to sources can be translated into the language of growth operations on rooted trees.

Last Updated on Monday, 13 June 2016 18:33

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