场论中的路径积分导论

PartⅠNon-RelativisticQuantumTheory

1、ThePathIntegralinQuantumTheory

1.1PropagatoroftheSchrSdingerEquation

1.2PropagatorasPathIntegral

1.3QuadraticHamiltonians

1.3.1CartesianMetric

1.3.2Non-CartesianMetric

1.4ClassicalInterpretation

2、PerturbationTheory

2.1FreePropagator

2.2PerturbativeExpansion

2.3ApplicationtoScattering

3、GeneratingFunctionals

3.1Groundstate-to-GroundstateTransitions

3.1.1GeneratingFunctional

3.2FunctionalDerivativesofGs-GsTransitionAmplitudes

PartⅡRelativisticQuantumFieldTheory

4、RelativisticFields

4.1EquationsofMotion

4.1.1Examples

4.2SymmetriesandConservationLaws

4.2.1GeometricalSpace-TimeSymmetries

4.2.2InternalSymmetries

5、PathIntegralsforScalarFields

5.1GeneratingFunctionalforFields

5.1.1EuclideanRepresentation

6、EvaluationofPathIntegrals

6.1FreeScalarFields

6.1.1GeneratingFunctional

6.1.2FeynmanPropagator

6.1.3GaussianIntegration

6.2InteractingScalarFields

6.2.1StationaryPhaseApproximation

6.2.2NumericalEvaluationofPathIntegrals

6.2.3RealTimeFormalism

7、TransitionRatesandGreensFunctions

7.1ScatteringMatrix

7.2ReductionTheorem

7.2.1CanonicalFieldQuantization

7.2.2DerivationoftheReductionTheorem

8、GreensFunctions

8.1n-pointGreensFunctions

8.1.1MomentumRepresentation

8.1.2OperatorRepresentations

8.2FreeScalarFields

8.2.1WicksTheorem

8.2.2FeynmanRules

8.3InteractingScalarFields

8.3.1PerturbativeExpansion

9、Perturbativeφ4Theory

9.1PerturbativeExpansionoftheGeneratingFunction

9.1.1GeneratingFunctionaluptoΟ(g)

9.2Two-PointFunction

9.2.1TermsuptoΟ(g0)

9.2.2TermsuptoΟ(g)

9.2.3TermsuptoΟ(g2)

9.3Four-PointFunction

9.3.1TermsuptoΟ(g)

9.3.2TermsuptoΟ(g2)

9.4Divergencesinn-PointFunctions

9.4.1PowerCounting

9.4.2DimensionalRegularizationofφ4Theory

9.4.3Renormalization

10、GreensFunctionsforFermions

10.1GrassmannAlgebra

10.1.1Derivatives

10.1.2Integration

10.2GreensFunctionsforFermions

10.2.1GeneratingFunctionalforFermions

10.2.2ReductionTheoremforFermions

10.2.3GreensFunctions

11、InteractingFields

11.1FeynmanRules

11.1.1FermionLoops

11.2WicksTheorem

11.3BosonizationofYukawaTheory

11.3.1PerturbativeExpansion

PartⅢGaugeFieldTheory

12、PathIntegralsforQED

12.1GaugeInvarianceinAbelianFreeFieldTheories

12.2GeneratingFunctional

12.3GaugeInvarianceinQED

12.4FeynmanRulesofQED

13PathIntegralsforGaugeFields

13.1Non-AbelianGaugeFields

13.2GeneratingFunctional

13.3GaugeFixingofL

13.4Faddeev-PopovDeterminant

13.4.1ExplicitFormsoftheFPDeterminant

13.4.2GhostFields

13.5FeynmanRules

14ExamplesforGaugeFieldTheories

14.1QuantumChromodynamics

14.2ElectroweakInteractions

UnitsandMetric

A.1Units

A.2MetricandNotation

Functionals

B.1Definition

B.2FunctionalIntegration

B.2.1GaussianIntegrals

B.3FunctionalDerivatives

RenormalizationIntegrals

GaussianGrassmannIntegration

References

Index

　　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。