The combinatorics of Green＇s functions in planar field theories-中国期刊网

摘要 Theaimofthisexpositionistoprovideadetaileddescriptionoftheuseofcombinatorialalgebrainquantumfieldtheoryintheplanarsetting.ParticularemphasisisplacedontherelationsbetweendifferenttypesofplanarGreen＇sfunctions.TheprimaryobjectisaHopfalgebrathatisnaturallydefinedonvariablesrepresentingnon-commutingsources,andwhosecoproductsplitsintotwohalf-coproducts.Thelattergiverisetothenotionofanunshuffiebialgebra.ThissettingallowsadescriptionoftherelationbetweenfullandconnectedplanarGreen＇sfunctionstobegivenbysolvingasimplelinearfixedpointequation.Wealsoincludeabriefoutlineoftheconsequencesofourapproachintheframeworkofordinaryquantumfieldtheory.

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The combinatorics of Green＇s functions in planar field theories

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The combinatorics of Green＇s functions in planar field theories

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