凝聚态场论

Preface

1Fromparticlestofields

1.1Classicalharmonicchain:phonons

1.2Functionalanalysisandvariationalprinciples

1.3Maxwellsequationsasavariationalprinciple

1.4Quantumchain

1.5Quantumelectrodynamics

1.6Noetherstheorem

1.7Summaryandoutlook

1.8Problems

2Secondquantization

2.1Introductiontosecondquantization

2.2Applicationsofsecondquantization

2.3Summaryandoutlook

2.4Problems

3Feymnanpathintegral

3.1Thepathintegral:generalformalism

3.2Constructionofthepathintegral

3.3ApplicationsoftheFeynmanpathintegral

3.4Summaryandoutlook

3.5Problems

4Functionalfieldintegral

4.1Constructionofthemany-bodypathintegral

4.2Fieldintegralforthequantumpartitionfunction

4.3Fieldtheoreticalbosonization:acasestudy

4.4Summaryandoutlook

4.5Problems

5Perturbationtheory

5.1Generalstructuresandlow-orderexpansions

5.2Groundstateenergyoftheinteractingelectrongas

5.3Infinite-orderexpansions

5.4Summaryandoutlook

5.5Problems

6Brokensymmetryandcollectivephenomena

6.1Mean-fieldtheory

6.2Plasmatheoryoftheinteractingelectrongas

6.3Bose-Einsteincondensationandsuperfluidity

6.4Superconductivity

6.5Fieldtheoryofthedisorderedelectrongas

6.6Summaryandoutlook

6.7Problems

7Responsefunctions

7.1Crashcourseinmodemexperimentaltechniques

7.2Linearresponsetheory

7.3Analyticstructureofcorrelationfunctions

7.4Electromagneticlinearresponse

7.5Summaryandoutlook

7.6Problems

8Therenormalizationgroup

8.1Theone-dimensionalIsingmodel

8.2Dissipativequantumtunneling

8.3Renormalizationgroup:generaltheory

8.4RGanalysisoftheferromagnetictransition

8.5RGanalysisofthenonlinearo-model

8.6Berezinskii-Kosterlitz-Thoulesstransition

8.7Summaryandoutlook

8.8Problems

9Topology

9.1Example:particleonaring

9.2Homotopy

9.30-Terms

9.4Wess-Zuminoterms

9.5Chern-Simonsterms

9.6Summaryandoutlook

9.7Problems

Index

　　Theoreticalcondensedmatterphysicsdrawsheavilyandincreasinglyonthelanguageofquantumfieldtheory.Thisprimerisaimedatelevatinggraduatestudentsofcondensedmatterphysicstoalevelwheretheycanengageinindependentresearch.Itemphasizesthedevelopmentofmodemmethodsofclassicalandquantumfieldtheorywithapplicationsofinterestinbothexperimentalandtheoreticalcondensedmatterphysics.Topicscoveredincludesecondquantization,pathandfunctionalfieldintegration,mean-fieldtheoryandcollectivephenomena,therenormalizationgroup,andtopology.Conceptualaspectsandformalmethodologyareemphasizedanddeveloped,butthediscussionisrootedfirmlyinpracticalexperimentalapplication.Aswellasroutineexercises,thetextincludesextendedandchallengingproblems,withfullyworkedsolutions,designedtoprovideabridgebetweenformalmanipulationsandresearch-orientedthinking.