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Topology and Condensed Matter Physics

  • Somendra Mohan Bhattacharjee
  • Mahan Mj
  • Abhijit Bandyopadhyay

Part of the Texts and Readings in Physical Sciences book series (TRiPS, volume 19)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Topological Tools

    1. Front Matter
      Pages 23-23
    2. Somnath Basu, Atreyee Bhattacharya
      Pages 25-43
    3. Samik Basu, Soma Maity
      Pages 45-63
    4. Dheeraj Kulkarni
      Pages 65-77
    5. Kingshook Biswas, Soma Maity
      Pages 79-108
    6. Utsav Choudhury, Atreyee Bhattacharya
      Pages 109-141
    7. Bobby Ezhuthachan
      Pages 153-168
  3. Physics Problems

    1. Front Matter
      Pages 169-169
    2. Somendra M. Bhattacharjee
      Pages 171-216
    3. Somendra M. Bhattacharjee
      Pages 217-251
    4. R. Shankar
      Pages 253-279
    5. P. Ramadevi
      Pages 343-357
    6. Sergei Nechaev
      Pages 359-398
    7. Subhro Bhattacharjee
      Pages 439-470
    8. Ville Lahtinen, Jiannis K. Pachos
      Pages 471-500
  4. Back Matter
    Pages 501-507

About this book

Introduction

This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. 

The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail. 

Keywords

Topological Ideas Condensed Matter Set Topology Homotopy theory Homology Differential Topology Vector Bundles Quantum Geometry Abelian Groups The Knot Group

Editors and affiliations

  • Somendra Mohan Bhattacharjee
    • 1
  • Mahan Mj
    • 2
  • Abhijit Bandyopadhyay
    • 3
  1. 1.Institute of Physics BhubaneswarIndia
  2. 2.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Department of PhysicsRamakrishna Mission Vivekananda UniversityHowrahIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-6841-6
  • Copyright Information Springer Nature Singapore Pte Ltd. and Hindustan Book Agency 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-10-6840-9
  • Online ISBN 978-981-10-6841-6
  • Series Print ISSN 2366-8849
  • Series Online ISSN 2366-8857
  • Buy this book on publisher's site
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