Gregory L. Naber's Books

Topology, Geometry and Gauge fields

Interactions

By: Gregory L. Naber

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Topology, Geometry and Gauge fields

Interactions

By: Gregory L. Naber

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.

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Page Count

428

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144197895X

ISBN 13

9781441978950

Topology, Geometry, and Gauge Fields

Interactions

By: Gregory L. Naber

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Topology, Geometry, and Gauge Fields

Interactions

By: Gregory L. Naber

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Page Count

453

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Springer Science & Business Media

Published Date

ISBN 10

1475768508

ISBN 13

9781475768503

Spacetime and Singularities

An Introduction

By: Gregory L. Naber

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Spacetime and Singularities

An Introduction

By: Gregory L. Naber

An elementary introduction to the geometrical methods and notions used in special and general relativity. Emphasizes the ideas concerned with structure of space-time that play a role in Penrose-Hawking singularity theorems.

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Page Count

196

Publisher

Cambridge University Press

Published Date

ISBN 10

0521336120

ISBN 13

9780521336123

Topological Methods in Euclidean Spaces

By: Gregory L. Naber

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Topological Methods in Euclidean Spaces

By: Gregory L. Naber

Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.

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Page Count

276

Publisher

Courier Corporation

Published Date

ISBN 10

0486153444

ISBN 13

9780486153445

Quantum Mechanics

An Introduction to the Physical Background and Mathematical Structure

By: Gregory L. Naber

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Quantum Mechanics

An Introduction to the Physical Background and Mathematical Structure

By: Gregory L. Naber

This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.

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Page Count

570

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110751941

ISBN 13

9783110751949

The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

By: Gregory L. Naber

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The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

By: Gregory L. Naber

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.

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Page Count

276

Publisher

Courier Corporation

Published Date

ISBN 10

0486432351

ISBN 13

9780486432359

Topology, Geometry, and Gauge Fields

Foundations

By: Gregory Naber

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Topology, Geometry, and Gauge Fields

Foundations

By: Gregory Naber

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

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Page Count

428

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387949461

ISBN 13

9780387949468

The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

By: Gregory L. Naber

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The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity

By: Gregory L. Naber

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “... his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)

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Page Count

324

Publisher

Springer

Published Date

ISBN 10

1441978372

ISBN 13

9781441978370

Quantum Mechanics

An Introduction to the Physical Background and Mathematical Structure

By: Gregory L. Naber

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Quantum Mechanics

An Introduction to the Physical Background and Mathematical Structure

By: Gregory L. Naber

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Solve jigsaw puzzle

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Page Count

570

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110751941

ISBN 13

9783110751949

Topology, Geometry and Gauge fields

Foundations

By: Gregory L. Naber

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Topology, Geometry and Gauge fields

Foundations

By: Gregory L. Naber

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Solve jigsaw puzzle

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Page Count

454

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441972544

ISBN 13

9781441972545

Book's by Gregory L. Naber

Topology, Geometry and Gauge fields

Topology, Geometry and Gauge fields

Topology, Geometry, and Gauge Fields

Topology, Geometry, and Gauge Fields

Spacetime and Singularities

Spacetime and Singularities

Topological Methods in Euclidean Spaces

Topological Methods in Euclidean Spaces

Quantum Mechanics

Quantum Mechanics

The Geometry of Minkowski Spacetime

The Geometry of Minkowski Spacetime

Topology, Geometry, and Gauge Fields

Topology, Geometry, and Gauge Fields

The Geometry of Minkowski Spacetime

The Geometry of Minkowski Spacetime

Quantum Mechanics

Quantum Mechanics

Topology, Geometry and Gauge fields

Topology, Geometry and Gauge fields

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