本书是关于经典场和量子场路径积分的初级读本，写作风、格简明扼要，重点介绍量子场的路径积分。本书介绍了场论最、新发展的基本理论，可以作为一学期强化课程的教材使用。场、论的路径积分方法有助于严格研究一些基本数学问题及其在强子物理、粒子物理和核物理中的应用，本书可供数学专业和理、论物理专业的学生使用。本书是对作者《场、对称性和夸克》、(Springer，1999)一书的补充，需要读者具有相对论量子力、学方面的知识。

本书是《国外物理名著系列》之一。本书几乎涉及了近代物理学中场论中的路径积分导引的所有领域，既有阐述学科基本理论的经典名著，也有反映某一学科专题前沿的专著。基础理论方面强调“经典”，选择了那些经得起时间检验、对物理学的发展产生重要影响、现在还不“过时”的著作；反映物理学某一领域进展的方面强调“前沿”和“热点”，根据国内物理学研究发展的实际情况，选择了能够体现相关学科最新进展，对有关方向的科研人员和研究生有重要参考价值的图书。本书还对部分目录标题和练习题进行了少量的翻译和注释，以方便国内读者的阅读和理解。

Part Ⅰ Non-Relativistic Quantum Theory

1、The Path Integral in Quantum Theory

 1.1 Propagator of the SchrSdinger 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 Amplitudes

Part Ⅱ 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

 6.1 Free Scalar Fields

6.1.1 Generating Functional

6.1.2 Feynman Propagator

6.1.3 Gaussian Integration

 6.2 Interacting Scalar Fields

6.2.1 Stationary Phase Approximation

6.2.2 Numerical Evaluation of Path Integrals

6.2.3 Real Time Formalism

7、Transition Rates and Green's Functions

 7.1 Scattering Matrix

 7.2 Reduction Theorem

7.2.1 Canonical Field Quantization

7.2.2 Derivation of the Reduction Theorem

8、Green's Functions

 8.1 n-point Green's Functions

8.1.1 Momentum Representation

8.1.2 Operator Representations

 8.2 Free Scalar Fields

8.2.1 Wick's Theorem

8.2.2 Feynman Rules

 8.3 Interacting Scalar Fields

8.3.1 Perturbative Expansion

9、Perturbative φ4 Theory

 9.1 Perturbative Expansion of the Generating Function

9.1.1 Generating Functional up to Ο(g)

 9.2 Two-Point Function

9.2.1 Terms up to Ο(g0)

9.2.2 Terms up to Ο(g)

9.2.3 Terms up to Ο(g2)

 9.3 Four-Point Function

9.3.1 Terms up to Ο(g)

9.3.2 Terms up to Ο(g2)

 9.4 Divergences in n-Point Functions

9.4.1 Power Counting

9.4.2 Dimensional Regularization of φ4 Theory

9.4.3 Renormalization

10、Green's Functions for Fermions

 10.1 Grassmann Algebra

10.1.1 Derivatives

10.1.2 Integration

 10.2 Green's Functions for Fermions

10.2.1 Generating Functional for Fermions

10.2.2 Reduction Theorem for Fermions

10.2.3 Green's Functions

11、Interacting Fields

 11.1 Feynman Rules

11.1.1 Fermion Loops

 11.2 Wick's Theorem

 11.3 Bosonization of Yukawa Theory

11.3.1 Perturbative Expansion

Part Ⅲ Gauge Field Theory

12、Path Integrals for QED

 12.1 Gauge Invariance in Abelian Free Field Theories

 12.2 Generating Functional

 12.3 Gauge Invariance in QED

 12.4 Feynman Rules of QED

13 Path Integrals for Gauge Fields

 13.1 Non-Abelian Gauge Fields

 13.2 Generating Functional

 13.3 Gauge Fixing of L

 13.4 Faddeev-Popov Determinant

13.4.1 Explicit Forms of the FP Determinant

13.4.2 Ghost Fields

 13.5 Feynman Rules

14 Examples for Gauge Field Theories

 14.1 Quantum Chromodynamics

 14.2 Electroweak Interactions

Units and Metric

 A.1 Units

 A.2 Metric and Notation

Functionals

 B.1 Definition

 B.2 Functional Integration

B.2.1 Gaussian Integrals

 B.3 Functional Derivatives

Renormalization Integrals

Gaussian Grassmann Integration

References

Index