Central Library

A brief introduction to topology and differential geometry in condensed matter physics / (Record no. 82880)

000 -LEADER
fixed length control field 08744nam a2200817 i 4500
001 - CONTROL NUMBER
control field 9780750339551
003 - CONTROL NUMBER IDENTIFIER
control field IOP
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20230516170257.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m eo d
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cn |||m|||a
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 211206s2021 enka fob 000 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780750339551
Qualifying information ebook
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780750339544
Qualifying information mobi
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780750339537
Qualifying information print
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780750339568
Qualifying information myPrint
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1088/978-0-7503-3955-1
Source of number or code doi
035 ## - SYSTEM CONTROL NUMBER
System control number (CaBNVSL)thg00082866
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1288247152
040 ## - CATALOGING SOURCE
Original cataloging agency CaBNVSL
Language of cataloging eng
Description conventions rda
Transcribing agency CaBNVSL
Modifying agency CaBNVSL
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QC20
Item number .P573 2021eb
072 #7 - SUBJECT CATEGORY CODE
Subject category code PHFC
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code SCI077000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 530.15
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Pires, A.
Fuller form of name (Antonio),
Relator term author.
9 (RLIN) 70647
245 12 - TITLE STATEMENT
Title A brief introduction to topology and differential geometry in condensed matter physics /
Statement of responsibility, etc. Antonio Sergio Teixeira Pires.
250 ## - EDITION STATEMENT
Edition statement Second edition.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
Name of producer, publisher, distributor, manufacturer IOP Publishing,
Date of production, publication, distribution, manufacture, or copyright notice [2021]
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (various pagings) :
Other physical details illustrations (some color).
336 ## - CONTENT TYPE
Content type term text
Source rdacontent
337 ## - MEDIA TYPE
Media type term electronic
Source isbdmedia
338 ## - CARRIER TYPE
Carrier type term online resource
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement [IOP release $release]
490 1# - SERIES STATEMENT
Series statement IOP ebooks. [2021 collection]
500 ## - GENERAL NOTE
General note "Version: 202111"--Title page verso.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc. note Includes bibliographical references.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 1. Path integral approach -- 1.1. Path integral -- 1.2. Path integral in quantum field theory -- 1.3. Spin -- 1.4. Path integral and statistical mechanics -- 1.5. Fermion path integral
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 2. Topology and vector spaces -- 2.1. Topological spaces -- 2.2. Group theory -- 2.3. Cocycle -- 2.4. Vector spaces -- 2.5. Linear maps -- 2.6. Dual space -- 2.7. Scalar product -- 2.8. Metric space -- 2.9. Tensors -- 2.10. p-Vectors and p-forms -- 2.11. Edge product -- 2.12. Pfaffian
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 3. Manifolds and fiber bundle -- 3.1. Manifolds -- 3.2. Lie algebra and Lie groups -- 3.3. Homotopy -- 3.4. Particle in a ring -- 3.5. Functions on manifolds -- 3.6. Tangent space -- 3.7. Cotangent space -- 3.8. Push-forward -- 3.9. Fiber bundle -- 3.10. Magnetic monopole -- 3.11. Tangent bundle -- 3.12. Vector field
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 4. Metric and curvature -- 4.1. Metric in a vector space -- 4.2. Metric in manifolds -- 4.3. Symplectic manifold -- 4.4. Exterior derivative -- 4.5. The Hodge * operator -- 4.6. The pull-back of a one-form -- 4.7. Orientation of a manifold -- 4.8. Integration on manifolds -- 4.9. Stokes' theorem -- 4.10. Homology -- 4.11. Cohomology -- 4.12. Degree of a map -- 4.13. Hopf-Poincar�e theorem -- 4.14. Connection -- 4.15. Covariant derivative -- 4.16. Curvature -- 4.17. The Gauss-Bonnet theorem -- 4.18. Surfaces -- 4.19. Geodesics -- 4.20. Fundamental theorem of the Riemann geometry
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 5. Dirac equation and gauge fields -- 5.1. The Dirac equation -- 5.2. Two-dimensional Dirac equation -- 5.3. Electrodynamics -- 5.4. Time reversal -- 5.5. Gauge field as a connection -- 5.6. Chern classes -- 5.7. Abelian gauge fields -- 5.8. Non-Abelian gauge fields -- 5.9. Chern numbers for non-Abelian gauge fields -- 5.10. Maxwell equations using differential forms
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 6. Berry connection and particle moving in a magnetic field -- 6.1. Introduction -- 6.2. Berry phase -- 6.3. The Aharonov-Bohm effect -- 6.4. Non-Abelian Berry connections -- 6.5. The Aharonov-Casher effect
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 7. Quantum Hall effect -- 7.1. Integer quantum Hall effect -- 7.2. Currents at the edge -- 7.3. Kubo formula -- 7.4. The quantum Hall state on a lattice -- 7.5. Particle on a lattice -- 7.6. The TKNN invariant -- 7.7. Quantum spin Hall effect -- 7.8. Chern-Simons action -- 7.9. The fractional quantum Hall effect
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 8. Topological insulators -- 8.1. Two- and three-band insulators -- 8.2. Nielsen-Ninomiya theorem -- 8.3. Haldane model -- 8.4. Checkerboard lattice -- 8.5. States at the edge -- 8.6. The Z2 topological invariants -- 8.7. The Kane-Mele model -- 8.8. Three-dimensional topological insulators -- 8.9. Calculation of edge modes
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 9. Topological phases in one dimension -- 9.1. The Su-Schrieffer-Heeger model -- 9.2. Winding number and Zak phase -- 9.3. Finite chain -- 9.4. Alternative form of the SSH Hamiltonian -- 9.5. Localized states at a domain wall -- 9.6. The Ising chain in a transverse field -- 9.7. The Kitaev chain -- 9.8. Majorana fermion operators -- 9.9. Rashba spin-orbit superconductor in one dimension
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 10. Topological superconductors -- 10.1. Basics of superconductivity -- 10.2. Two-dimensional chiral p-wave superconductors -- 10.3. Two-dimensional chiral p-wave superconductor on a lattice -- 10.4. Continuum limit -- 10.5. Non-Abelian statistics -- 10.6. d-Wave pairing symmetry
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 11. Higher-order topological insulators -- 11.1. Crystalline symmetries -- 11.2. Second-order topological insulator in two dimensions -- 11.3. Gapless corner states -- 11.4. A three-dimensional chiral HOTI
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 12. Classification of topological states with symmetries -- 12.1. Symmetries -- 12.2. Time-reversal symmetry -- 12.3. Particle-hole symmetry -- 12.4. Chiral symmetry -- 12.5. Periodic table -- 12.6. Complex classes -- 12.7. Real classes -- 12.8. Classification for zero dimensions -- 12.9. Dirac Hamiltonians -- 12.10. Dimension reduction -- 12.11. Topological defects
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 13. Weyl semimetals -- 13.1. The Weyl equation -- 13.2. Linear Weyl modes -- 13.3. Chern numbers -- 13.4. An example -- 13.5. Fermi arcs -- 13.6. Weyl semimetal in an external magnetic field -- 13.7. Type II Weyl semimetals -- 13.8. Weyl semimetals with spins higher than 1/2 -- 13.9. Chiral anomaly -- 13.10. Dirac semimetals
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 14. Kubo theory and transport -- 14.1. Linear response theory -- 14.2. Electron transport -- 14.3. Anomalous Hall effect -- 14.4. Orbital magnetization -- 14.5. Spin transport -- 14.6. Interacting topological insulators
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 15. Magnetic models -- 15.1. One-dimensional antiferromagnetic model -- 15.2. Sine-Gordon soliton -- 15.3. Two-dimensional non-linear sigma model -- 15.4. XY model -- 15.5. Theta terms
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 16. Topological magnon insulators -- 16.1. Magnon Hall effect -- 16.2. The ferromagnetic honeycomb lattice -- 16.3. Generalized Bogoliubov transformation -- 16.4. Antiferromagnetic honeycomb lattice -- 16.5. Thermal Hall conductivity
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 17. K-theory -- 17.1. Rings -- 17.2. Equivalence relations -- 17.3. Grothendieck group -- 17.4. Sum of vector bundles -- 17.5. K-theory -- 17.6. K-theory and topological insulators -- 17.7. The 2Z invariant -- 17.8. The Atiyah-Singer index theorem.
520 3# - SUMMARY, ETC.
Summary, etc. This book provides a self-consistent introduction to the mathematical ideas and methods from these fields that will enable the student of condensed matter physics to begin applying these concepts with confidence. This expanded second edition adds eight new chapters, including one on the classification of topological states of topological insulators and superconductors and another on Weyl semimetals, as well as elaborated discussions of the Aharonov-Casher effect, topological magnon insulators, topological superconductors and K-theory.
530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE
Additional physical form available note Also available in print.
538 ## - SYSTEM DETAILS NOTE
System details note Mode of access: World Wide Web.
538 ## - SYSTEM DETAILS NOTE
System details note System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 ## - BIOGRAPHICAL OR HISTORICAL DATA
Biographical or historical data Antonio S.T. Pires graduated from the University of California in Santa Barbara in 1976. He is a Professor of Physics at the Universidade Federal de Minas Gerais, Brazil researching quantum field theory applied to condensed matter. He is a member of the Brazilian Academy of Science, was the Editor of the Brazilian Journal of Physics, and a member of the Advisory Board of the Journal of Physics: Condensed Matter. He has published the books ADS/CFT correspondence in condensed matter and theoretical tools for spin models in magnetic systems.
588 0# - SOURCE OF DESCRIPTION NOTE
Source of description note Title from PDF title page (viewed on December 6, 2021).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Mathematical physics.
9 (RLIN) 11013
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Condensed matter
General subdivision Mathematics.
9 (RLIN) 21163
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Topology.
9 (RLIN) 13470
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Geometry, Differential.
9 (RLIN) 70648
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Condensed matter physics (liquid state & solid state physics)
Source of heading or term bicssc
9 (RLIN) 70144
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Condensed matter.
Source of heading or term bisacsh
9 (RLIN) 17064
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element Institute of Physics (Great Britain),
Relator term publisher.
9 (RLIN) 11622
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
International Standard Book Number 9780750339537
-- 9780750339568
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title IOP (Series).
Name of part/section of a work Release 21.
9 (RLIN) 70649
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title IOP ebooks.
Name of part/section of a work 2021 collection.
9 (RLIN) 70650
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://iopscience.iop.org/book/978-0-7503-3955-1">https://iopscience.iop.org/book/978-0-7503-3955-1</a>
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type eBooks

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