Overview
- Introduces topology with mathematical rigour while remaining accessible to physicists
- Contains compilation of the lectures delivered at the SERC school, India
- Bridges the language barrier among the disciplines of physics, and between physics and mathematics
- Includes supplementary material: sn.pub/extras
Part of the book series: Texts and Readings in Physical Sciences (TRiPS, volume 19)
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Table of contents (18 chapters)
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Front Matter
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Physics Problems
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Front Matter
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Keywords
About this book
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.
Editors and Affiliations
About the editors
MAHAN MJ is a professor of mathematics at the Tata Institute of Fundamental Research, Mumbai, India, and a monk of the Ramakrishna Mission. Earlier, he was a professor of mathematics and dean of research at the Ramakrishna Mission Vivekananda University until 2015. He joined the PhD program in mathematics at the University of California, U.S.A. He is a recipient of the 2011 Shanti Swarup Bhatnagar Award in Mathematical Sciences and the Infosys Science Foundation Award 2015 for Mathematical Sciences. He specialises in geometric topology and hyperbolic geometry.
ABHIJIT BANDYOPADHYAY is an associate professor of Physics at Ramakrishna Mission Vivekananda University, Belur, Howrah, India. He specialises in high energy physics and cosmology.
Bibliographic Information
Book Title: Topology and Condensed Matter Physics
Editors: Somendra Mohan Bhattacharjee, Mahan Mj, Abhijit Bandyopadhyay
Series Title: Texts and Readings in Physical Sciences
DOI: https://doi.org/10.1007/978-981-10-6841-6
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. and Hindustan Book Agency 2017
Hardcover ISBN: 978-981-10-6840-9Published: 31 January 2018
Softcover ISBN: 978-981-13-4958-4Published: 11 December 2018
eBook ISBN: 978-981-10-6841-6Published: 20 December 2017
Series ISSN: 2366-8849
Series E-ISSN: 2366-8857
Edition Number: 1
Number of Pages: XXVIII, 507
Number of Illustrations: 68 b/w illustrations, 80 illustrations in colour
Topics: Mathematical Physics, Mathematical Applications in the Physical Sciences, Condensed Matter Physics