Path Integrals in Quantum Mechanics (Oxford Graduate Texts) 1st Edition by Jean Zinn-Justin | (PDF) Free Download

Description

The main goal of this work is to familiarize the reader with a tool, the path integral, that offers an alternative point of view on quantum mechanics, but more important, under a generalized form, has become the key to a deeper understanding of quantum field theory and its applications, which extend 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.Path integrals are powerful tools for the study of quantum mechanics, because 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 and simple calculations of physical quantities in the semi-classical limit. We will illustrate this observation with scattering processes, spectral properties or barrier penetration.The formulation of quantum mechanics based on path integrals, if it seems mathematically more complicated than the usual formulation based on partial differential equations, is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is supremely clear. As always, path integrals can seem very unrigorous to the uninitiated, but Jean Zinn-Justin makes a lot of effort to highlight the mathematical subtleties. Expressions are clearly indexed, the notation is careful and not sloppy. This makes line by line careful study very rewarding. The other great aspect of the book is its emphasis on euclidean path integrals formulation, which makes relation to statistical mechanics and stochastic process much clearer. Some might say the notation is pedantic, but for someone learning the topic for the first time, I prefer to keep all the factors correctly so I can get the results confidently. For people who want careful math derivations, this book is great!

⭐This title is a very detailed and formal introduction to path integrals in quantum mechanics. In my opinion, it is a great book that differs from the usual exposition of the subject, which is biased towards particle physics. The material contained is very similar to that in Zinn-Justin’s other book, “Quantum Field Theory and Critical Phenomena”, but the discussions are more focused towards quantum and statistical physics, and does not include much about QFT. Exercises come with solutions, and the minimum requirements on quantum mechanics are contained in an appendix.

⭐Adatto a chi già a delle basi molto buone in QFT, va però considerato come una introduzione a un volume precedente dello stesso autore, in cui sviluppa il metodo del Path integral in fisica delle particelle.Approfondito ma impegnativo.Absence totale de sens pédagogique. On devine beaucoup de travail et d’efforts.Il faut s’accrocher, ce que la concurrence permet d’éviter.

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