Abstract
For Yang-Mills theory in the Minkowski space it is proved that the constraint set is a smooth submanifold of the phase space consisting of square integrable Cauchy data.
Similar content being viewed by others
References
Segal, I.: The Cauchy problem for the Yang-Mills equations. J. Funct. Anal.33, 175–194 (1979)
Ginibre, J., Velo, G.: The Cauchy problem for coupled Yang-Mills and scalar fields in temporal gauge. Commun. Math. Phys.82, 1–28 (1981)
Eardley, D., Moncrief, V.: The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties. Commun. Math. Phys.83, 171–191 (1982)
Eardley, D., Moncrief, V. The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. II. Completion of proof. Commun. Math. Phys.83, 193–212 (1982)
Moncrief, V.: Gribov degeneracies: coulomb gauge condition and initial value constraints. J. Math. Phys.20, 579–585 (1979)
Binz, E., Śniatycki, J., Fischer, A.: Geometry of classical fields. Amsterdam: North-Holland 1988
Arms, J.: The structure of the solution set for the Yang-Mills equations. Math. Proc. Camb. Phil. Soc.90, 361–372 (1981)
Arms, J., Marsden, J., Moncrief, V.: Symmetry and bifurcation of momentum mappings. Commun. Math. Phys.78, 455–478 (1981)
Marsden, J., Weinstein, A.: Reduction of sympletic manifolds with symmetry. Rep. Math. Phys.5, 121–130 (1974)
Kato, T.: Perturbation theory for linear operators, 2nd (ed.). Berlin, Heidelberg, New York: Springer 1984
Adams, R.: Sobolev spaces. Orlando, Florida: Academic Press 1975
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Partially supported by the NSERC Operating Grant No. A8091
Rights and permissions
About this article
Cite this article
Śniatycki, J. Regularity of constraints in the Minkowski space Yang-Mills theory. Commun.Math. Phys. 141, 593–597 (1991). https://doi.org/10.1007/BF02102818
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02102818