Abstract
We formulate a general theory of conservation laws and other invariants for a physical system through equivalence relations. The conservation laws are classified according to the type of equivalence relation, with group equivalence, homotopical equivalence, and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the Abelian symmetries are shown to be stable through application of well-known theorems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. G. O. Freundet al., J. Math. Phys. 16, 433 (1975).
D. Finkelstein,J. Math. Phys. 7, 1218 (1966).
G. 't Hooft,Nucl. Phys. B79, 276 (1974).
K. T. Shah,Ann. Inst. Henri Poincaré 25, 177 (1976);
K. T. ShahRep. Math. Phys. 6, 171 (1974),
Topic in bifurcation theory, Universität Clausthal, seminar report (1973).
H. Osborn,Ann. Inst. Fourier 14, 71 (1974).
R. Thom,Stabilité Structurelle et Morphogenèse (Benjamin, 1972).
M. Golubitsky and V. Guillemin,Stable Mappings and Their Singularities (Springer-Verlag, 1973).
Abdus Salam and J. Strathdee, ICTP, Trieste, preprint IC/76/62 (1976).
Abdus Salam and J. Strathdee,Nature 252, 569 (1974).
K. T. Shah,Lett. Nuovo Cim. 18, 156 (1977).
K. T. Shah,Phys. Lett. 63A, 4 (1977).
K. T. Shah, On the violation of conservation laws due to non-Abelian symmetries (to appear).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shah, K.T. A general theory of conservation laws, their violation, and spontaneous phenomena. Found Phys 9, 271–282 (1979). https://doi.org/10.1007/BF00715183
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00715183