Abstract
The role of boundary conditions for Yang-Mills fields in spatially bounded domains is examined. It is shown that the conservation laws and the structure of the constraints depend on the choice of boundary conditions. The difficulties due to lack of any existence and uniqueness theorems for mixed problems in Yang-Mills theory are discussed.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Bohin: Quantum Theory (Prentice Hall, New York, 1952)
M. MacCallum: “Quantum Cosmological Models", in Quantum Gravity, ed. by C. Isham, R. Penrose, and D.W. Sciama (Clarendon Press, Oxford, 1973)
B. Lawruk, J. Śniatycki, W.M. Tulczyjew: “Special Symplectic Spaces”, J. Diff. Eq. 17 477–497 (1974)
J. Kijowski and W. M. Tulczyjew, A Symplectic Framework for Field Theories, Springer Lecture Notes in Physics 107 (Springer, Berlin, 1979)
E. Binz, J. Śniatycki: “Conservation Laws in Spacetimes with Boundary”, Class. Q. Grav. 3 1191–1197 (1986)
E. Binz, J. Śniatycki, H. Fischer: Geometry of Classical Fields (North Holland, 1988)
J. Kijowski: “On Energy Localization in Gauge Field Theories and Gravitation”, lecture at 22nd Symposium on Mathematical Physics, Toruń, December 1989
I. Segal: “The Cauchy Problem for the Yang-Mills Equations”, J. Funct. Anal. 33 175–194 (1979)
J. Ginibre, G. Velo: “The Cauchy Problem for Coupled Yang-Mills and Scalar Fields in the Temporal Gauge”, Commun. Math. Phys. 82 1–21 (1981)
D. Eardley, V. Moncrief: “The Global Existence of Yang-Mills-Higgs Fields in 4Dimensional Minkowski space”, Commun. Math. Phys. 83 171–179 (1982)
I. Segal: “Non-Linear Semi-Groups”, Ann. Math. 78 339–364 (1963)
J. Śniatycki, K. Foltinek, G. Bolton: “Perturbation Approach to the Mixed Problem for Yang-Mills Equations” (unpublished)
Th. De Donder: “Theorie invariantive du calcul des variations”, Bull. Acad. de. Belg. (1929)
J. Śniatycki: “On the Geometric Structure of Classical Field Theory in Lagrangian Formulation”, Proc. Camb. Phil. Soc. 68 475–483 (1970)
C. Günther: “The Polysymplectic Hamiltonian Formalism in Field Theory and the Calculus of Variations”, J. Diff. Geom. 25 23–53 (1987)
Th. Lepage: Acad. Roy. Belg. Bull. (Cl. Sci. V.) 22 716 (1936)
J. Arms: “The Structure of the Solution Set for the Yang-Mills Equations”, Math. Proc. Camb. Phil. Soc. 90 361–372 (1981)
J. Arms: J. Marsden, V. Moncrief: “Symmetry and Bifurcations of Momentum Mappings”, Commun. Math. Phys. 78 455–478 (1981)
A. Jaffe, C. Taubes: Vortices and Monopoles: Structure of Static Gauge Theories (Birkhauser, Boston, 1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Śniatycki, J. (1991). On boundary conditions for Yang-Mills fields in spatially bounded domains. In: Hennig, JD., Lücke, W., Tolar, J. (eds) Differential Geometry, Group Representations, and Quantization. Lecture Notes in Physics, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53941-7_3
Download citation
DOI: https://doi.org/10.1007/3-540-53941-7_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53941-4
Online ISBN: 978-3-540-46473-0
eBook Packages: Springer Book Archive