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Graphs in Perturbation Theory - Algebraic Structure and Asymptotics (Hardcover, 1st ed. 2018)
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Graphs in Perturbation Theory - Algebraic Structure and Asymptotics (Hardcover, 1st ed. 2018)
Series: Springer Theses
Expected to ship within 10 - 15 working days
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This book is the first systematic study of graphical enumeration
and the asymptotic algebraic structures in perturbative quantum
field theory. Starting with an exposition of the Hopf algebra
structure of generic graphs, it reviews and summarizes the existing
literature. It then applies this Hopf algebraic structure to the
combinatorics of graphical enumeration for the first time, and
introduces a novel method of asymptotic analysis to answer
asymptotic questions. This major breakthrough has combinatorial
applications far beyond the analysis of graphical enumeration. The
book also provides detailed examples for the asymptotics of
renormalizable quantum field theories, which underlie the Standard
Model of particle physics. A deeper analysis of such renormalizable
field theories reveals their algebraic lattice structure. The
pedagogical presentation allows readers to apply these new methods
to other problems, making this thesis a future classic for the
study of asymptotic problems in quantum fields, network theory and
far beyond.
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