Knots and Feynman diagrams /
Kreimer, Dirk, 1960-
Knots and Feynman diagrams / Knots & Feynman Diagrams Dirk Kreimer. - Cambridge : Cambridge University Press, 2000. - 1 online resource (xii, 259 pages) : digital, PDF file(s). - Cambridge lecture notes in physics ; 13 . - Cambridge lecture notes in physics ; 13. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalization, early chapters discuss the rationality of ladder diagrams and simple link diagrams. The necessary basics of knot theory are then presented and the number-theoretic relationship between the topology of Feynman diagrams and knot theory is explored. Later chapters discuss four-term relations motivated by the discovery of Vassiliev invariants in knot theory and draw a link to algebraic structures recently observed in noncommutative geometry. Detailed references are included. Dealing with material at perhaps the most productive interface between mathematics and physics, the book will be of interest to theoretical and particle physicists, and mathematicians.
9780511564024 (ebook)
Quantum field theory.
Knot theory.
Feynman diagrams.
QC174.52.K56 / K74 2000
530.14/3
Knots and Feynman diagrams / Knots & Feynman Diagrams Dirk Kreimer. - Cambridge : Cambridge University Press, 2000. - 1 online resource (xii, 259 pages) : digital, PDF file(s). - Cambridge lecture notes in physics ; 13 . - Cambridge lecture notes in physics ; 13. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalization, early chapters discuss the rationality of ladder diagrams and simple link diagrams. The necessary basics of knot theory are then presented and the number-theoretic relationship between the topology of Feynman diagrams and knot theory is explored. Later chapters discuss four-term relations motivated by the discovery of Vassiliev invariants in knot theory and draw a link to algebraic structures recently observed in noncommutative geometry. Detailed references are included. Dealing with material at perhaps the most productive interface between mathematics and physics, the book will be of interest to theoretical and particle physicists, and mathematicians.
9780511564024 (ebook)
Quantum field theory.
Knot theory.
Feynman diagrams.
QC174.52.K56 / K74 2000
530.14/3