場(chǎng)論中的路徑積分導(dǎo)引

內(nèi)容概要

本書是關(guān)于經(jīng)典場(chǎng)和量子場(chǎng)路徑積分的初級(jí)讀本，寫作風(fēng)格簡(jiǎn)明扼要，重點(diǎn)介紹量子場(chǎng)的路徑積分。本書介紹了場(chǎng)論最新發(fā)展的基本理論，可以作為一學(xué)期強(qiáng)化課程的教材使用。場(chǎng)論的路徑積分方法有助于嚴(yán)格研究一些基本數(shù)學(xué)問題及其在強(qiáng)子物理、粒子物理和核物理中的應(yīng)用，本書可供數(shù)學(xué)專業(yè)和理論物理專業(yè)的學(xué)生使用。本書是對(duì)作者《場(chǎng)、對(duì)稱性和夸克》（Springer，1999）一書的補(bǔ)充，需要讀者具有相對(duì)論量子力學(xué)方面的知識(shí)。

作者簡(jiǎn)介

作者：(德國(guó))莫澤爾(Mosel.U.)

書籍目錄

Part Ⅰ Non-Relativistic Quantum Theory  1 The Path Integral in Quantum Theory    1.1 Propagator of the Schrodinger Equation    1.2 Propagator as Path Integral    1.3 Quadratic Hamiltonians       1.3.1 Cartesian Metric      1.3.2 Non-Cartesian Metric    1.4 Classical Interpretation  2 Perturbation Theory    2.1 Free Propagator    2.2 Perturbative Expansion    2.3 Application to Scattering  3 Generating Functionals    3.1 Groundstate-to-Groundstate Transitions      3.1.1 Generating Functional    3.2 Functional Derivatives of Gs-Gs Transition AmplitudesPartⅡ Relativistic Quantum Field Theory  4 Relativistic Fields    4.1 Equations of Motion      4.1.1 Examples    4.2 Symmetries and Conservation Laws      4.2.1 Geometrical Space-Time Symmetries      4.2.2 Internal Symmetries  5 Path Integrals for Scalar Fields    5.1 Generating Functional for Fields      5.1.1 Euclidean Representation  6 Evaluation of Path Integrals  7 Transition Rates and Green's Functions  8 Green's Functions  9 Perturbative Theory  10 Green's Functions for Fermions  11 Interacting FieldsPart Ⅲ Gauge Field Theory  12 Path Integrals for QED  13 path Integrals for Gauge Fields  14 Examples for Gauge Field TheoriesUnits and MetricFunctionalsRenormalization IntegralsGaussian Grassmann IntegrationReferencesIndes

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