Topology, Geometry, and Gauge Fields Foundations
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathe
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Editors J.E. Marsden L. Sirovich M . Golubitsky W. Jager F. John (deceased) Advisor G.Iooss
Springer Science+Business Media, LLC
Texts in Applied Mathematics 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Sirovich: Introduction to Applied Mathematics . Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos . Hale/Korak: Dynamics and Bifurcations. Chorin/Marsden: A Mathematical Introduction to Fluid Mechanics , 3rd ed. Hubbard/West: Differential Equations: A Dynamical Systems Approach : Ordinary Differential Equations. Sontag: Mathematical Control Theory: Deterministic Finite Dimensional Systems. Perko: Differential Equations and Dynamical Systems, 2nd ed. Seaborn: Hypergeometric Functions and Their Applications . Pipkin: A Course on Integral Equations. Hoppensteadt/Peskin: Mathematics in Medicine and the Life Sciences. Braun: Differential Equations and Their Applications, 4th ed. Stoerlllulirsch: Introduction to Numerical Analysis, 2nd ed. Renardy/Rogers: A First Graduate Course in Partial Differential Equations. Banks: Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. Brenner/Scott: The Mathematical Theory of Finite Element Methods . Van de Velde: Concurrent Scientific Computing . Marsden/Ratiu: Introduction to Mechanics and Symmetry. Hubbard/West: Differential Equations: A Dynamical Systems Approach: Higher-Dimensional Systems. Kaplan/Glass: Understanding Nonlinear Dynamics . Holmes: Introduction to Perturbation Methods. Curtain/Zwart: An Introduction to Infinite-Dimensional Linear Systems Theory. Thomas: Numerical Partial Differential Equations: Finite Difference Methods. Taylor: Partial Differential Equations: Basic Theory. Merkin: Introduction to the Theory of Stability. Naber: Topology, Geometry, and Gauge Fields: Foundations.
Gregory L . Naber
Topology, Geometry, and Gauge Fields Foundations
With 55 Illustrations
,
Springer
Gregory L. Naber Department of Mathematics and Statistics California State University, Chico Chico, CA 95929-0525 USA
Series Editors J.E. Marsden Control and Dynamical Systems, 116-81 California Institute of Technology Pasadena, CA 91125 USA
L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA
M. Golubitsky Department of Mathematics University of Houston Houston , TX 77204-3476 USA
w.Jager Department of Applied Mathematics Universitat Heidelberg Irn Neuenheimer Feld 294 69120 Heidelberg, Germany
Mathematics Subject Classification (1991) : 22E70, 58G05, 81T13, 53C80 , 58B30 , 81-99 Library of Congress Cataloging-in-Publication Data Naber , Gregory L., 1948Topology, geometry, and gauge fields : foundations / Gregory L. Naber. p. ern . - (Texts in applied mathematics; 25) Includes bibliographical references and index . 1. Topology . 2. Geometry . 3. Gauge fields (Physics) 4. Mathematical physics. I. Title . II. Series . QC20 .7.T65N33 1997 516.3 '62 -dc21 96-49166 Printed on acid-free paper.
© 1997 Springer Science+Business Media New York Originally publi
