凝聚態(tài)物理學(xué)中的量子場論

前言

　　The objective of this book is to familiarize the reader with the recent achievements ofquantum field theory （henceforth abbreviated as QFT）. The book is oriented primarilytowards condensed matter physicists but， I hope， can be of some interest to physicists inother fields. In the last fifteen years QFT has advanced greatly and changed its languageand style. Alas， the fruits of this rapid progress are still unavailable to the vast democraticmajority of graduate students， postdoctoral fellows， and even those senior researchers whohave not participated directly in this change. This cultural gap is a great obstacle to thecommunication of ideas in the condensed matter community. The only way to reduce thisis to have as many books covering these new achievements as possible. A few good booksalready exist; these are cited in the select bibliography at the end of the book. Havingstudied them I found， however， that there was still room for my humble contribution. Inthe process of writing I have tried to keep things as simple as possible; the amount offormalism is reduced to a minimum. Again， in order to make life easier for the newcomer， Ibegin the discussion with such traditional subjects as path integrals and Feynman diagrams.It is assumed， however， that the reader is already familiar with these subjects and thecorresponding chapters are intended to refresh the memory. I would recommend those whoare just starting their research in this area to read the first chapters in parallel with someintroductory course in QFT. There are plenty of such courses， including the evergreen bookby Abrikosov， Gorkov and Dzyaloshinsky. I was trained with this book and thoroughlyrecommend it.　　Why study quantum field theory？ For a condensed matter theorist as， I believe， for otherphysicists， there are several reasons for studying this discipline. The first is that QFT providessome wonderful and powerful tools for our research， The results achieved with these toolsare innumerable; knowledge of their secrets is a key to success for any decent theorist.The second reason is that these tools are also very elegant and beautiful. This makes theprocess of scientific research very pleasant indeed. I do not think that this is an accidentalcoincidence; it is my strong belief that aesthetic criteria are as important in science asempirical ones. Beauty and truth cannot be separated， because beauty is truth realized（Viadimir Solovyev）. The history of science strongly supports this belief： all great physicaltheories are at the same time beautiful.

內(nèi)容概要

This book is a course in modern quantum field theory as seen through the eyes of a theoristworking in condensed matter physics. It contains a gentle introduction to the subject andcan therefore be used even by graduate students. The introductory parts include a deriva-tion of the path integral representation, Feynman diagrams and elements of the theory ofmetals including a discussion of Landau Fermi liquid theory. In later chapters the discus-sion gradually turns to more advanced methods used in the theory of strongly correlatedsystems. The book contains a thorough exposition of such nonperturbative techniques as1/N-expansion, bosonization （Abelian and non-Abelian）, conformal field theory and theoryof integrable systems. The book is intended for graduate students, postdoctoral associatesand independent researchers working in condensed matter physics.

書籍目錄

Preface to the first editionPreface to the second editionAcknowledgements for the first editionAcknowledgements for the second editionⅠ Introduction to methods  1 QFT:language and goals  2 Connection between quantum and classical: path integrals  3 Definitions of correlation functions: Wick's theorem  4 Free bosonic field in an external field  5 Perturbation theory: Feynman diagrams  6 Calculation methods for diagram series: divergences and their elimination  7 Renormalization group procedures  8 O(N)-symmetric vector model below the transition point  9 Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion  10 0(3) nonlinear sigma model in the strong coupling limitⅡ Fermions  11 Path integral and Wick's theorem for fermions  12 Interacting electrons: the Fermi liquid  13 Electrodynamics in metals  14 Relativistic fermions: aspects of quantum electrodynamics (1+1)-Dimensional quantum electrodynamics (Schwinger model)  15 Aharonov-Bohm effect and transmutation of statistics  The index theorem  Quantum Hall ferromagnetⅢ Strongly fluctuagng spin systems  Introduction  16 Schwinger-Wigner quantization procedure: nonlinear sigma models  Continuous field theory for a ferromagnet  Continuous field theory for an antiferromagnet  17 O(3) nonlinear sigma model in (2 + 1) dimensions: the phase diagram  Topological excitations: skyrmions  18 Order from disorder  19 Jordan-Wigner transformation for spin S = 1/2 models in D = 1, 2, 3  20 Majorana representation for spin S =1/2 magnets: relationship to Z2  lattice gauge theories  21 Path integral representations for a doped antiferromagnet  N Physics in the world of one spatial dimension  Introduction  22 Model of the free bosonic massless scalar field  23 Relevant and irrelevant fields  24 Kosterlitz-Thouless transition  25 Conformal symmetry  Gaussian model in the Hamiltonian formulation  26 Virasoro algebra  Ward identities  Subalgebra sl(2)  27 Differential equations for the correlation functions  Coulomb gas construction for the minimal models  28 Ising model  Ising model as a minimal model  Quantum lsing model  Order and disorder operators Correlation functions outside the critical point Deformations of the Ising model  29 One-dimensional spinless fermions: Tomonaga-Luttinger liquid  Single-electron correlator in the presence of Coulomb interaction  Spin S = 1/2 Heisenberg chain  Explicit expression for the dynamical magnetic susceptibility  30 One-dimensional fermions with spin: spin-charge separation  Bosonic form of the SU1 (2) Kac-Moody algebra  Spin S = 1/2 Tomonaga-Luttinger liquid  Incommensurate charge density wave  Half-filled band  31 Kac-Moody algebras: Wess-Zumino——Novikov-Witten model  Knizhnik-Zamolodchikov (KZ) equations  Conformal embedding  SUI(2) WZNW model and spin S = 1/2 Heisenberg antiferromagnet  SU2(2) WZNW model and the Ising model  32 Wess-Zumino-Novikov-Witten model in the Lagrangian form:  non-Abelian bosonization  33 Semiclassical approach to Wess-Zumino-Novikov-Witten models  34 Integrable models: dynamical mass generation  General properties of integrable models  Correlation functions: the sine-Gordon model  Perturbations of spin S = 1/2 Heisenberg chain: confinement  35 A comparative study of dynamical mass generation in one and three dimensions  Single-electron Green's function in a one-dimensional charge density wave state  36 One-dimensional spin liquids: spin ladder and spin S = 1 Heisenberg chain  Spin ladder  Correlation functions  Spin S = 1 antiferromagnets  37 Kondo chain  38 Gauge fixing in non-Abelian theories: (1+1)-dimensional quantumchromodynamics  Select bibliography  Index

章節(jié)摘錄

　　The related problem is a long-standing problem of the Kondo lattice or, in more generalwords, the problem of the coexistence of conduction electrons and local magnetic moments.We have discussed this problem very briefly in Chapter 21, where it was mentioned that thisremains one of the biggest unsolved problems in condensed matter physics. The only part ofit which is well understood concerns a situation where localized electrons are representedby a single local magnetic moment （the Kondo problem）. In this case we know that thelocal moment is screened at low temperatures by conduction electrons and the ground stateis a singlet. The formation of this singlet state is a nonperturbative process which affectselectrons very far from the impurity. The relevant energy scale （the Kondo temperature） isexponentially small in the exchange coupling constant. It still remains unclear how conduc-tion and localized electrons reconcile with each other when the local moments are arrangedregularly （Kondo lattice problem）. Empirically, Kondo lattices resemble metals with verysmall Fermi energies of the order of several degrees. It is widely believed that conductionand localized electrons in Kondo lattices hybridize at low temperatures to create a singlenarrow band （see the discussion in Chapter 21）. However, our understanding of the detailsof this process remains vague. The most interesting problem is how the localized electronscontribute to the volume of the Fermi sea （according to the large-N approximation, they docontribute）. The most dramatic effect of this contribution is expected to occur in systemswith one conduction electron and one spin per unit cell. Such systems must be insulators（the so-called Kondo insulator）.The available experimental data apparently support thispoint of view: all compounds with an odd number of conduction electrons per spin areinsulators （Aeppli and Fisk, 1992）. At low temperatures they behave as semiconductorswith very small gaps of the order of several degrees. The marked exception is FeSi wherethe size of the gap is estimated as——,700 K （Schlesinger et al., 1993）.

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    凝聚態(tài)物理學(xué)中的量子場論 PDF格式下載

---