Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-29T03:03:32.329Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 June 2012

Theodore Frankel
Affiliation:
University of California, San Diego
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
The Geometry of Physics
An Introduction
, pp. 671 - 674
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[A, M, R] Abraham, R., Marsden, J., and Ratiu, T.Manifolds, Tensor Analysis, and Applications, Addison Wesley, 1983Google Scholar
[A, S] Aharonov, V., and Susskind, L.Observability of the sign change of spinors under 2π rotations. Phys. Rev. 158 (1967), 1237–38CrossRefGoogle Scholar
[A] Arnold, V, I.Mathematical Methods of Classical Mechanics, Springer, 1978CrossRefGoogle Scholar
[A2] Arnold, V, I.Ordinary Differential Equations. M.I.T. Press, 1978Google Scholar
[B, S] Bamberg, P. and Sternberg, S.A Course in Mathematics for Students of Physics, vol. 2, Cambridge, 1990Google Scholar
[B] Berry, M.Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A 392 (1984), pp. 45–57CrossRefGoogle Scholar
[B, K, G] Blank, A., Friedrichs, K., and Grad, H.Notes on Magneto-Hydrodynamics, part V, N.Y.U. notes, (1957)Google Scholar
[Bl] Bleecker, David.Gauge Theory and Variational Principles, Addison Wesley, 1981Google Scholar
[B, T] Bott, R. and Tu, L.Differential forms in Algebraic Topology, Springer, 1982CrossRefGoogle Scholar
[Bo] Bott, R.Lectures on Morse theory, old and new. Bul. Amer. Math. Soc. 7 (1982) pp. 331–358CrossRefGoogle Scholar
[Bo2] Bott, R.On induced representations. Proc. Symp. in Pure Math. 48 (1988), pp. 1–13.CrossRefGoogle Scholar
[Boy] Boyling, J.B.An axiomatic approach to classical thermodynamics, Proc. R. Soc., London, A 329 (1972), pp. 35–70CrossRefGoogle Scholar
[Br] Brillouin, L.Tensors in Mechanics and Elasticity, Academic Press, 1964Google Scholar
[Ca] Cartan, E.On Manifolds with an Affine Connection and the Theory of Relativity, Bibliopolis, 1986Google Scholar
[C] Coleman, S.Aspects of Symmetry, Cambridge, 1985CrossRefGoogle Scholar
[C, J] Courant, R. and John, F.Introduction to Calculus and Analysis, vol. 2, Wiley-Interscience, 1974Google Scholar
[Do] Do Carmo, M.Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976Google Scholar
[D, F] Driver, B. and Frankel, T.On the growth of waves on manifolds, J. Math. Anal. Appl. 178 (1993), pp. 143–55CrossRefGoogle Scholar
[D, S] Duff, G. and Spencer, D.Harmonic tensors on Riemannian manifolds with boundary, Ann. Math. 56 (1952), pp. 128–56CrossRefGoogle Scholar
[E] Eckmann, B.Harmonische Funktionen und Randwertaufgaben in einem Komplex. Comm. Math. Helv. 17 (1945), pp. 240–55.CrossRefGoogle Scholar
[Fe] Felsager, B.Geometry, Particles and Fields, Odense University Press, 1981
[F] Feynman, R.Q.E.D. Princeton, 1985
[FF] Feynman, R.. Theory of Fundamental Processes, Benjamin, 1961Google Scholar
[F, L, S] Feynman, R., Leighton, R. and Sands, M.The Feynman Lectures on Physics, Vols I, II and III, Addison Wesley, 1964Google Scholar
[F, W] Feynman, R. and Weinberg, S.Elementary Particles and the Laws of Physics, Cambridge, 1987
[Fl] Flanders, H.Differential Forms, Academic Press, 1963Google Scholar
[Fr] Frankel, T.Gravitational Curvature, W.H. Freeman, 1979Google Scholar
[Fr 2] Frankel, T.Critical submanifolds of the classical groups and Stiefel manifolds, in Differential and Combinatorial Topology, Edited by Stewart, Cairns, Princeton, 1965Google Scholar
[Fk] Friedrichs, K.Differential forms on Riemannian manifolds, Comm. Pure and Appl. Math. 8 (1955), pp. 551–90CrossRefGoogle Scholar
[Ga] Galloway, G.A generalization of Myers' theorem and an application to relativistic cosmology, J. Diff. Geom. 14, pp. 105–116, 1979CrossRefGoogle Scholar
[G, F] Gelfand, I. and Fomin, S.Calculus of Variations, Prentice-Hall, 1963Google Scholar
[G, H] Greenberg, M. and Harper, J.Algebraic Topology, Benjamin, 1981Google Scholar
[G] Grossman, N.Holonomic measurables in geodesy. J. Geophysical Res. 79. (1974), pp. 689–94CrossRefGoogle Scholar
[G, P] Guillemin, V. and Pollack, A.Differential Topology, Prentice-Hall, 1974Google Scholar
[H] Hermann, R.Differential Geometry and the Calculus of Variations, 2nd ed., Mathematical Science Press, 1977Google Scholar
[H, O] Hehl, F.H. and Obukhov, Y.N.Foundations of Classical Electrodynamics, Birkhaüser, 2003CrossRefGoogle Scholar
[H, Y] Hocking, J. and Young, G.Topology, Addison-Wesley, 1961Google Scholar
[Hs] Hsiang, W. Y.Lectures on Lie Groups, World Scientific, 2000CrossRefGoogle Scholar
[I, Z] Itzykson, C. and Zuber, J-B.Quantum Field Theory, McGraw-Hill, 1980Google Scholar
[Ka] Kato, T.Perturbation Theory for Linear Operators, Springer, 1976Google Scholar
[K] Kobayashi, S.Fixed points of isometries, Nag. Math. J. 13 (1959), pp. 63–68CrossRefGoogle Scholar
[K, N] Kobayashi, S. and Nomizu, K.Foundations of Differential Geometry, vols. 1 and 2. Wiley, New York, 1963Google Scholar
[L] Lawson, B.Minimal Varieties in Real and Complex Geometries. Presses de L'Université Montréal, 1974Google Scholar
[L-S, K] Levi Setti, R. and Lasinski, T.Strongly Interacting Particles, University of Chicago Press, 1973Google Scholar
[M, H] Marsden, J. and Hughes, T.Mathematical Foundations of Elasticity, Prentice-Hall, 1983Google Scholar
[Mi] Michel, L.Symmetry defects and broken symmetry. Rev. Mod. Phys. 51 (1980), pp. 617–51CrossRefGoogle Scholar
[M] Milnor, J.Morse Theory, Princeton University Press, 1963Google Scholar
[M2] Milnor, J.Topology from the Differentiable Viewpoint, University Press of Virginia, 1965Google Scholar
[M, S] Milnor, J. and Stasheff, J.Characteristic Classes, Princeton, 1974Google Scholar
[M, T, W] Misner, C., Thorne, K., and Wheeler, J.Gravitation, Freeman, 1970
[Mo] Moffat, H.The degree of unknottedness of tangled vortex lines, J. Fluid Mech. 35 (1969), pp. 117–129CrossRefGoogle Scholar
[Mu] Murnaghan, F. D.Finite Deformation of an Elastic Solid, Dover, 1951, republished 1967Google Scholar
[Nam] Nambu, Y.Quarks, World Scientific, 1985
[N, S] Nash, C. and Sen, S.Topology and Geometry for Physicists, Academic Press, 1983Google Scholar
[N] Nelson, E.Tensor Analysis, Princeton University Press, 1967Google Scholar
[No] Nomizu, K.Lie Groups and Differential Geometry, Math. Soc. Japan, 1956Google Scholar
[O] Osserman, R.Poetry of the Universe, Anchor Books, 1995Google Scholar
[R] Rabin, J.Introduction to quantum field theory for mathematicians, in Geometry and Quantum Field Theory, Edited by D., Fried and K., Uhlenbeck, Amer. Math Soc. 1995, pp. 183–269CrossRefGoogle Scholar
[Ro] Roe, J.Elliptic Operators, Topology and Asymptotic Methods, Longman, 1988Google Scholar
[Sam] Samelson, H.Topology of Lie Groups, Bul. Amer. Math. Soc. 58 (1952), pp. 2–37Google Scholar
[Sam H] Samelson, H.Differential forms, the early days. Amer. Math. Monthly, 108 (2001) pp. 522–30CrossRefGoogle Scholar
[S] Simmons, G.Topology and Modern Analysis, McGraw-Hill, 1963Google Scholar
[Si] Simon, B.Holonomy, the quantum adiabatic theorem, and Berry's phase. Phys, Rev. 51 (1983), pp. 2167–70Google Scholar
[Sp] Spivak, M.A Comprehensive Introduction to Differential Geometry, (5 volumes) Publish or Perish Press, 1979Google Scholar
[St] Steenrod, N.Topology of Fiber Bundles, Princeton University Press, 1951CrossRefGoogle Scholar
[Sto] Stong, C.L. The amateur scientist, Scientific American 233 (December 1975), pp. 120–5
[Su] Sudbery, A.Quantum Mechanics and the Particles of Nature, Cambridge, 1986Google Scholar
[Sy] Sniatycki, J.Quantization of charge. J. Math. Phys. 15 (1974), pp. 619–20.CrossRefGoogle Scholar
['t Hooft] 't Hooft, G.In Search of the Ultimate Building Blocks, Cambridge, 1997Google Scholar
[T] Truesdell, C.The influence of elasticity on analysis: the classic heritage. Bul. Amer. Math. Soc. 9 (1983), pp. 293–310CrossRefGoogle Scholar
[T, T] Truesdell, C. and R., Toupin, R. The Classical Field Theories, Handbuch der Physik, III–I, 1960Google Scholar
[Wd] Wald, R.General Relativity, University of Chicago Press, 1984CrossRefGoogle Scholar
[Wa] Warner, F.Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman, 1971Google Scholar
[We] Weinberg, S.The Quantum Theory of Fields, Vol II, Cambridge, 1996CrossRefGoogle Scholar
[Wy] Weyl, H.The Theory of Groups and Quantum Mechanics, Dover, 1950Google Scholar
[W] Whittaker, E.A History of the Theories of Aether and Electricity, vol. 1, Harper, 1960
[Z] Zhang, D.Yang and contemporary mathematics. Math. Intelligencer 15 (1993), pp. 13–21CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Theodore Frankel, University of California, San Diego
  • Book: The Geometry of Physics
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139061377.033
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Theodore Frankel, University of California, San Diego
  • Book: The Geometry of Physics
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139061377.033
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Theodore Frankel, University of California, San Diego
  • Book: The Geometry of Physics
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139061377.033
Available formats
×