×

Topology and physics. (English) Zbl 1414.81013

Hackensack, NJ: World Scientific (ISBN 978-981-327-849-3/hbk; 978-981-327-850-9/pbk; 978-981-327-868-4/ebook). vii, 222 p. (2019).

Show indexed articles as search result.

Publisher’s description: Since its birth in Poincaré’s seminal 1894 “Analysis Situs”, topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably – resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences – finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.
In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between “Topology” and “Physics”. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
The articles of this volume will be reviewed individually.
Indexed articles:
Atiyah, M. F.; Manton, N. S., Complex geometry of nuclei and atoms, 1-16 [Zbl 1432.81069]
Dijkgraaf, Robbert; Witten, Edward, Developments in topological gravity, 17-80 [Zbl 1421.81158]
Kauffman, Louis H., Majorana fermions and representations of the braid group, 81-108 [Zbl 1421.81057]
Kim, Minhyong, Arithmetic gauge theory: a brief introduction, 109-134 [Zbl 1451.14113]
Penrose, Roger, Singularity theorems, 135-171 [Zbl 1429.83047]
Wang, Zhenghan, Beyond anyons, 173-180 [Zbl 1426.82063]
Wen, Xiao-Gang, Four revolutions in physics and the second quantum revolution – a unification of force and matter by quantum information, 181-204 [Zbl 1421.81009]
Zhang, Haijun; Zhang, Shou-Cheng, Topological insulators from the perspective of first-principles calculations, 205-214 [Zbl 1459.82315]
Yang, Chen Ning; Zhang, S. C., Appendix: \(\mathrm{SO}_4\) symmetry in a Hubbard model, 215-222 [Zbl 1427.82062]

MSC:

81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
82-06 Proceedings, conferences, collections, etc. pertaining to statistical mechanics
81Qxx General mathematical topics and methods in quantum theory
81Txx Quantum field theory; related classical field theories
83E05 Geometrodynamics and the holographic principle
00A79 Physics
00B15 Collections of articles of miscellaneous specific interest
PDFBibTeX XMLCite
Full Text: DOI