×

zbMATH — the first resource for mathematics

Gauge theories of gravitation. A reader with commentaries. With a foreword by T. W. B. Kibble. (English) Zbl 1282.83046
Hackensack, NJ: World Scientific; London: Imperial College Press (ISBN 978-1-84816-726-1/hbk). xvii, 635 p. (2013).
There were very successful developments in the field of gauge theory that led to a unification of the theories of electromagnetic, weak and strong interactions. Only the gravitational interaction described by Einstein’s theory of general relativity (GR) stands outside, it could not be incorporated into this framework. Despite the fact that first ideas on gauge theory stem from a mathematical analysis of GR and that some features of GR resemble those of gauge theory, today it is generally accepted that GR is no theory of the same type as the other gauge-field theories of fundamental interactions. For, such a theory had to start from the rigid symmetry groups and the respective conserved currents provided by the Lagrange-Noether formalism in the Minkowski space-time and introduce compensating (i.e., gauge) fields by a localization of the rigid symmetry groups – what is not the case for the gravitational field as described by GR. The editors of this book, who are prominent researchers in this field, share the expectation with other theorists that “a full clarification of the gauge dynamics of gravity might be the last missing link to the hidden structure of a consistent unification of all the fundamental interactions at both the classical and the quantum level”. And so, the book leads the reader from early ideas on gauge theory (Part A) over Poincaré gauge theory of gravity (Part B) to extensions of the latter theory (Part C). The text is completed by Part D, wherein specific subjects of metric-affine gravity and Poincaré gauge theory are considered. The latter includes chapters devoted to the relationship of dislocations in crystals to the torsion of a 3d differential manifold (one of the editors [FWH] took part in these studies, too). The foreword is written by Tom Kibble, who is one of the fathers of the gauge theory of gravity. The book documents how two great developments of theoretical physics were brought together: the gauge theory and a great class of geometrical generalizations of GR. On more than 600 pages, one finds at the beginning of each of the 19 chapters a commentary by the editors which is followed by reprints of founding and survey articles concerning the respective topic and providing a guide to additional literature. The volume also contains (sometimes only some pages of) papers having another character; they however contribute to a deeper understanding of the whole topic. There are also passages in the commentaries and a brief chapter, where ‘fallacies’ in other papers and textbooks are indicated, what contributes to the readability of the book.
The editors recommend the reader first to study “our introductory commentaries and become familiar with the basic ideas, then to read specific reprints, and after that to return to our text, explore the additional literature, etc.” The volume is an excellent guide for students, who – as the editors say – want to “gain insight through self-study into gauge theories of gravity within a relatively short period of time” and for university lecturers, who perform seminars on this topic. Last but not least, it is very useful for researchers, who intend to win an overview over different roots and aims of such theories; it also could motivate them to turn themselves in their own work to this field.

MSC:
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C40 Gravitational energy and conservation laws; groups of motions
81-03 History of quantum theory
01A75 Collected or selected works; reprintings or translations of classics
53C05 Connections (general theory)
53C80 Applications of global differential geometry to the sciences
83C35 Gravitational waves
00A79 Physics
83-03 History of relativity and gravitational theory
01A60 History of mathematics in the 20th century
PDF BibTeX XML Cite
Full Text: DOI