Path Integrals in Quantum Mechanics (Paperback)

Jean Zinn-Justin

  • 出版商: Oxford University
  • 出版日期: 2010-09-03
  • 售價: $1,050
  • 貴賓價: 9.8$1,029
  • 語言: 英文
  • 頁數: 336
  • 裝訂: Paperback
  • ISBN: 0198566751
  • ISBN-13: 9780198566755
  • 相關分類: 量子 Quantum
  • 下單後立即進貨 (約5~7天)

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商品描述

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 Schrodinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.

商品描述(中文翻譯)

本書的主要目標是讓讀者熟悉一種工具,即路徑積分,它提供了量子力學的另一種觀點,更重要的是,在一種廣義形式下,它成為了深入理解量子場論及其應用的關鍵,這些應用從粒子物理學延伸到相變或量子氣體的性質。

路徑積分是數學對象,可以被視為對無限多個變數(由路徑表示)的一般化,相對於常規積分。它們具有常規積分的代數性質,但從分析的角度來看,具有新的性質。

路徑積分是研究量子力學的強大工具,因為它們非常明確地強調了經典力學和量子力學之間的對應關係。物理量被表示為對所有可能路徑的平均值,但在半經典極限下,主要貢獻來自接近經典路徑的路徑。因此,路徑積分在半經典極限下對於物理量的直觀理解和簡單計算非常有用。我們將通過散射過程、光譜性質或障壁穿透等示例來說明這一觀察結果。

基於路徑積分的量子力學表述,雖然在數學上比基於偏微分方程的常規表述更複雜,但對於具有許多自由度的系統非常適用,而薛定諤類型的形式主義則不太有用。它可以簡單地構建玻色子和費米子的多體理論。