Abstract
The relationships between topological charge quantization, Lagrangians and various cohomology theories are studied. A very general criterion for charge quantization is developed and applied to various physical models. The relationship between cohomology and homotopy is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dirac, P.A.M.: Quantized singularities in the electromagnetic field, Proc. R. Soc. Lond. A133, 60 (1931)
Witten, E.: Global aspects of current algebra. Nucl. Phys. B223, 422 (1983)
Wess, J., Zumino, B.: Consequences of anomalous ward identities. Phys. Lett.37B, 95 (1971)
Deser, S., Jackiw, R., Templeton, S.: Topologically massive gauge theories. Ann. Phys.140, 372 (1982)
Deser, S., Jackiw, R., Templeton, S.: Three dimensional massive gauge theories. Phys. Rev. Lett.48, 975 (1982)
Schoenfeld, J.: A mass term for three dimensional gauge fields. Nucl. Phys. B185, 157 (1981)
Siegel, W.: Unextended superfields in extended supersymmetry. Nucl. Phys. B156, 135 (1979)
Bagger, J., Witten, E.: Quantization of Newton's constant in certain supergravity theories. Phys. Lett.115B, 202 (1982)
Bott, R., Tu, L.: Differential forms in algebraic topology. Berlin, Heidelberg, New York: Springer 1982
Wu, T.T., Yang, C.N.: Dirac's monopole without strings: classical Lagrangian theory. Phys. Rev. D14, 437 (1976)
Feynman, R.P., Hibbs, A.R.: Quantum mechanics and path integrals. New York: McGraw-Hill 1965
Zumino, B.: Chiral anomalies and differential geometry. In: Relativity, groups and topology. II. DeWitt, B.S., Stora, R. eds. Amsterdam: North-Holland 1984
Singer, I.M., Thorpe, J.: Lecture notes on elementary topology and geometry. Berlin, Heidelberg, New York: Springer 1967
Misner, C., Thorne, K., Wheeler, J.A.: Gravitation. San Francisco, Freeman 1970
Eguchi, T., Gilkey, P.B., Hanson, A.J.: Gravitation, gauge theories and differential geometry. Phys. Rept.66, 213 (1980)
Spanier, E.H.: Algebraic topology. New York: McGraw-Hill 1966
Nash, J., Sen, S.: Topology and geometry for physicists, London: Academic Press 1983
Rabinovici, E., Schwimmer, A., Yankielowicz, S.: Quantization in the presence of Wess-Zumino Terms. WIS-84/30-PH
Witten, E.: Curent algebra, baryons, and quark confinement. Nucl. Phys. B223, 433 (1983)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
This work was supported in part by the National Science Foundation under Contracts PHY 81-18547; and by the Director, Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contracts DE-AC03-76SF00098
Alfred P. Sloan Foundation Fellow
Rights and permissions
About this article
Cite this article
Alvarez, O. Topological quantization and cohomology. Commun.Math. Phys. 100, 279–309 (1985). https://doi.org/10.1007/BF01212452
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01212452