A Combinatorial Perspective on Quantum Field Theory

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book A Combinatorial Perspective on Quantum Field Theory by Karen Yeats, Springer International Publishing
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Author: Karen Yeats ISBN: 9783319475516
Publisher: Springer International Publishing Publication: November 23, 2016
Imprint: Springer Language: English
Author: Karen Yeats
ISBN: 9783319475516
Publisher: Springer International Publishing
Publication: November 23, 2016
Imprint: Springer
Language: English

This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory.  Among the outcomes are both physical insights and interesting mathematics.

The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras.  The remainder is broken into two parts.  The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical.  The second part looks at Feynman graphs and their periods.

The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.

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This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory.  Among the outcomes are both physical insights and interesting mathematics.

The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras.  The remainder is broken into two parts.  The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical.  The second part looks at Feynman graphs and their periods.

The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.

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