Abstract
We deal with the geometrical foundations of a covariant scheme, which is developed to give a “co-ordinate independent” perturbation expansion ofSU(2)×SU(2) chiral theories with pions and nucleons. The pion fields play the role of local co-ordinates on a 3-D manifold with constant curvature in isospace. The presence of the nucleon isospinor field forces us to deal with the problem of endowing the manifold with a spin structure. In this way the nucleon isospinor is accommodated in the fiber space of the principal fiber bundle of the tangent bundle of the manifold.
Similar content being viewed by others
References
Meetz, K.: J. Math. Phys.10, 589 (1969)
Honerkamp, J.: Nucl. Phys. B36, 130 (1972)
Ecker, G., Honerkamp, J.: Nucl. Phys. B52, 211 (1973)
Daniel, M., Horgan, R. R.: Desy 74/2 preprint
Steenrod, N.: The topology of fibre bundles. Princeton: Univ. Press 1951
Milnor, J.W., Stasheff, J.D.: Characteristic Classes, Annals of Mathematics Studies. Princeton: Univ. Press 1974
Lichnerowicz, A.: Topics on Space-Time, Battelle Recontres: 1967 Lectures in Mathematics and Physics. New York: Benjamin 1968
Milnor, J.W.: L'Enseignment Math.9, 198 (1963)
Author information
Authors and Affiliations
Additional information
Communicated by R. Haag
Rights and permissions
About this article
Cite this article
Daniel, M. The geometry of a covariant expansion in chiral theories with nucleons. Commun.Math. Phys. 49, 97–106 (1976). https://doi.org/10.1007/BF01608734
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01608734