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Theoretical condensed matter physics draws heavily and increasingly on the language of quantum field theory. This primer is aimed at elevating graduate students of condensed matter physics to a level where they can engage in independent research. It emphasizes the development of modem methods of classical and quantum field theory with applications of interest in both experimental and theoretical condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized and developed, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking.

Preface

Fromparticlestofields

.Classicalharmonicchain-phonons

.2Functionalanalysisandvariationalprinciples

.3Maxwellsequationsasariationalprinciple

.4Quantumchain

.5Quantumelectrodynamics

.6Noetherstheorem

.7Summaryandoutlook

.8Problems

2Secondquantization

2.Introductiontosecondquantization

2.2Applicationsofsecondquantization

2.3Summaryandoutlook

2.4Problems

3Feymnanpathintegral

3.Thepathintegral-generalformalism

3.2Constructionofthepathintegral

3.3ApplicationsoftheFeynmanpathintegral

3.4Summaryandoutlook

3.5Problems

4Functionalfieldintegral

4.Constructionofthemany-bodypathintegral

4.2Fieldintegralforthequantumpartitionfunction

4.3Fieldtheoreticalbosonization-acasestudy

4.4Summaryandoutlook

4.5Problems

5Perturbationtheory

5.Generalstructuresandlow-orderexpansions

5.2Groundstateenergyoftheinteractingelectrongas

5.3Infinite-orderexpansions

5.4Summaryandoutlook

5.5Problems

6Bro

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

书籍介绍

Theoretical condensed matter physics draws heavily and increasingly on the language of quantum field theory. This primer is aimed at elevating graduate students of condensed matter physics to a level where they can engage in independent research. It emphasizes the development of modem methods of classical and quantum field theory with applications of interest in both experimental and theoretical condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized and developed, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking.