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Combinatorics and the Feynman Identity: Applications of Combinatorial Analysis to the Feynman Identity - Couverture souple

LIN, MINGSHR

 
9783639178210: Combinatorics and the Feynman Identity: Applications of Combinatorial Analysis to the Feynman Identity
Couverture souple
ISBN 10 : 3639178211 ISBN 13 : 9783639178210
Editeur : VDM Verlag, 2009

Synopsis

The book investigated the applications of combinatorics and graph theory in the analysis of the Feynman Identity of the partition function of the two dimensional Ising Model. Chapter one gives a general introduction to the partition function of the Ising Model and the Feynman Identity in the language of graph theory. Chapter two describes and proves combinatorially the Feynman Identity in a special case when there is only one vertex and multiple loops. Chapter three introduces a new way to calculate the number of cycles in a directed graph, along with its application in the special case discussed in chapter two to derive the analytical expression of the number of non-periodic cycles. Chapter four comes back to the general form of the Feynman Identity and several combinatorial identities are derived by introducing special conditions of the graph and applying the Feynman Identity under the condition. Chapter five concludes the work by summarizing the main idea in each chapter and provides insight for generalizations in three dimensional Ising Model.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The book investigated the applications of combinatorics and graph theory in the analysis of the Feynman Identity of the partition function of the two dimensional Ising Model. Chapter one gives a general introduction to the partition function of the Ising Model and the Feynman Identity in the language of graph theory. Chapter two describes and proves combinatorially the Feynman Identity in a special case when there is only one vertex and multiple loops. Chapter three introduces a new way to calculate the number of cycles in a directed graph, along with its application in the special case discussed in chapter two to derive the analytical expression of the number of non-periodic cycles. Chapter four comes back to the general form of the Feynman Identity and several combinatorial identities are derived by introducing special conditions of the graph and applying the Feynman Identity under the condition. Chapter five concludes the work by summarizing the main idea in each chapter and provides insight for generalizations in three dimensional Ising Model.

Biographie de l'auteur

MINGSHR MATT LIN earned his PhD degree at Caltech. His work specialized in applying physics intuition to calculations and proof in math. His visualization way of thinking has acquired him bird-view picture of his study. He is also enthusiastic about math and science education for high school and college students.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag
Date d'édition
2009
Langue
anglais
ISBN 10 
3639178211
ISBN 13 
9783639178210
Reliure
Broché
Nombre de pages
52
Coordonnées du fabricant
non disponible
Personne responsable
non disponible