Ângela Mestre

Hopf algebras and quantum field theory

Combinatorics of n-point functions via Hopf algebra

• Broschiertes Buch

Produktbeschreibung

In perturbative quantum field theory, the n-point functions consist, in general, of an infinity of Feynman graphs. Traditionally, these are generated via functional methods. This book describes the relation between complete, connected, and 1-particle irreducible n-point functions directly at the level of the Hopf algebra of time-ordered field operators. The ensembles of time-ordered n-point functions are simply linear forms on this algebra. It is showed, for instance, that the complete and connected n-point functions are elegantly related through the convolution product (induced by the coproduct). In this setting, a simple algebraic relation between connected and 1-particle irreducible n-point functions is derived, while the connected n-point functions are expressed in terms of their loop order contributions. At the center of the work stands a Hopf algebraic representation of graphs and a new algorithm to recursively generate all trees or all connected graphs and their values as Feynman graphs. This monograph presents a clear and self-contained exposition of all the results and their proofs. An introduction to the basic concepts required for the reading is also given.

Produktdetails

• Verlag: LAP Lambert Academic Publishing
• Aufl.
• Seitenzahl: 112
• Erscheinungstermin: 5. September 2012
• Englisch
• Abmessung: 220mm x 150mm x 7mm
• Gewicht: 168g
• ISBN-13: 9783659131738
• ISBN-10: 3659131733
• Artikelnr.: 36413844

Autorenporträt

Ângela Mestre received her Ph.D. in Physics from the University of Coimbra in February 2008.