相對論量子場論 (第2卷)-路徑積分形式體系 (英文) 9787576707533 (美)邁克爾.斯特里 克蘭

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書名:相對論量子場論 (第2卷)-路徑積分形式體系 (英文)
ISBN:9787576707533
出版社:哈爾濱工業大學
著編譯者:(美)邁克爾.斯特里 克蘭
叢書名:國外優秀物理著作原版系列
頁數:188
所在地:中國大陸 *此為代購商品
書號:1548615
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【台灣高等教育出版社簡體書】 相對論量子場論 (第2卷)-路徑積分形式體系 (英文) 787576707533 (美)邁克爾.斯特里 克蘭

內容簡介

在經典物理學中,引入場是為了構建因果和局部的物理定律,本書以引入場為主要內容,以《相對量子場論(第一卷》介紹的內容為基礎,重新使用了現代路徑積分形式,重點關注量子電動力學和色動力學的應用。全書分為8章,具體內容包括量子力學的路徑積分公式、標量場的路徑積分、費米子場的路徑積分、阿貝爾規範場的路徑積分、群與李群、量子色動力學的路徑積分公式、QCD的重正化、場論中的拓撲對象、異常的有效拉格朗日量、手征性異常的攝動理論等內容。

目錄

Preface
Acknowledgements
Author biography
Units and conventions
l Path integral formulation of quantum mechanics
1 1 The transition probability amplitude
1 2 Derivation of the quantum mechanical path integral
1 3 Path integral in terms of the Lagrangian
1 3 1 Summary
1 3 2 Caveats and clarmcatiOns
1 4 Computing simple path integrals
1 4 1 Free particle in the path integral formalism
1 4 2 Quantum harmonic oscillator in the path integral formalism
1 4 3 Path integral for deviations from the classical solution
1 4 4 Connection to our usual understanding of the quantum harmonic oscillator
1 4 5 Generalization to an arbitrary potential and the WKB approximation
1 5 Calculating time—ordered expectation values
1 6 Adding sources
1 7 Asymptotic states and vacuum---vacuum transitions
1 8 Generating functional and Green』S function for quadratic theories
1 8 1 Quantum harmonic oscillator
1 9 Euclidean path integral and the statistical mechanics partition function
1 9 1 Connection to statistical mechanics
References
2 Path integrals for scalar fields
2 1 Generating functional for a free real scalar field
2 2 Interacting real scalar field theory
2 2 1 Perturbative expansion ofλφ4
2 2 2 The two—point function
2 23 The four—point function
2 3 Generating functional for connected diagrams
2 4 The sell:energy
2 5 The effective action and vertex functions
2 6 Generating function for one—particle irreducible graphs
2 6 1 Scalar Schwinger—Dyson equation
2 7 Interacting complex scalar fields
References
3 Path integrals for fermionic fields
3 1 Finite—dimensional Grassmann algebra
3 1 1 Derivatives of Grassmann variables
3 1 2 Integrals over Grassmann variables
3 1 3 Gaussian integrals of Grassmann variables
3 1 4 Infinite—dimensional Grassmann algebra
3 2 Path integral for a free Dirac field
3 3 Path integral for an interacting Dirac field
3 4 Fermion loops
4 Path integrals for abelian gauge fields
4 1 Free abelian gauge theory
4 2 The photon propagator
4 3 Generating functional for abelian gauge fields in general Lorenz gauge
4 3 1 Faddeev-Popov gauge fixing preview
4 4 Generating functional for QED in general Lorenz gauge
4 5 General Lorenz—gauge QED generating functional to O(e2)
4 6 QED effective action and vertex functions
4 7 Ward—Takahashi identities
4 7 1 Relation between the electron—photon vertex and inverse electron propagator
4 7 2 Electron self-energy and the sub—leading vertex
4 7 3 Extension to higher orders
4 7 4 Implications for renormalization
5 Groups and Lie groups
5 1 Group theory basics
5 1 1 Subgroups
5 1 2 The group center
5 2 Examples
5 2 1 Finite groups
5 2 2 Infinite discrete groups
5 2 3 ContinuouS compact groups
5 3 RepresentatiOns of groups
5 3 1 Equivalent representations
5 3 2 Reducible and irreducible representations
5 3 3 Product representations
5 4 The group U(1)
5 5 The group SU(2)
5 6 The group SU(3)
5 6 1 Quadratic Casimir invariants
5 6 2 Cartan sub—algebra and ladder operators
5 6 3 Irreducible representations
5 6 4 The singlet—D00
5 6 5 The triplet and anti triplet—D10and D01
5 6 6 Higher dimensional representations
5 6 7 Product representations
S 7 The group su(N)
5 8 The Haar measure
5 8 1 General method for constructing invariant Haar measures
5 8 2 Haar measure example—SU(2)
References
6 Path integral formulation of quantum chromodynamics
6 1 The Fadeev—Popov method
6 1 1 General Lorenz gauge
6 1 2 Summary
6 2 QCD Feynman rules
6 2 1 Bare quark propagator
6 2 2 Bare gluon propagator
6 2 3 Bare ghost propagator
6 2 4 Quark-gluon vertex
6 2 5 Gluon s
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