Path integrals in quantum mechanics

Jean Zinn-Justin - Collection Oxford Graduate Texts

318 pages, parution le 18/11/2004

Ajouter à une liste

Indisponible

Résumé

The main goal of this book is to familiarize the reader with a tool, the path integral, that not only offers an alternative point of view on quantum mechanics, but more importantly, under a generalized form, has also become the key to a deeper understanding of quantum field theory and its applications, extending from particle physics to phase transitions or properties of quantum gases.

Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. They are powerful tools for the study of quantum mechanics, since they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding of physical quantities in the semi-classical limit, as well as simple calculations of such quantities.

This observation can be illustrated with scattering processes, spectral properties or barrier penetration effects. Even though the formulation of quantum mechanics based on path integrals seems mathematically more complicated than the usual formulation based on partial differential equations, the path integral formulation is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows simple construction of a many-body . theory both for bosons and fermions.

L'auteur - Jean Zinn-Justin

Jean Zinn-Justin est chercheur en physique théorique au CEA/Saclay et professeur de mathématiques associé à l'université de Paris VII. Ses travaux portent sur différentes applications de la théorie quantique des champs, de la théorie des transitions de phase en physique statistique à la physique des interactions fondamentales. Il est l'auteur d'un livre de théorie quantique des champs Quantum Field Theory and Critical Phenomena.

Autres livres de Jean Zinn-Justin

Groupes de symétrie en physique

Intégrale de chemin en mécanique quantique

Découvrir tous les livres de Jean Zinn-Justin

Sommaire

Gaussian integrals
Path integrals in quantum mechanics
Partition function and spectrum
Classical and quantum statistical physics
Path integrals and quantization
Path integrals and holomorphic formalism
Path integrals: fermions
Barrier penetration: semi-classical approximation
Quantum evolution and scattering matrix
Path integrals in phase space
Appendix: Quantum mechanics: minimal background
Bibliography
Index

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Jean Zinn-Justin
Collection	Oxford Graduate Texts
Parution	18/11/2004
Nb. de pages	318
Format	17 x 24,5
Couverture	Relié
Poids	689g
Intérieur	Noir et Blanc
EAN13	9780198566748
ISBN13	978-0-19-856674-8