Within the framework of classical (nonquantum) theory of topological transitions, the problem of singularities is discussed; this is one of the basic obstacles to transition to a quantum description. The features of the solution of this problem for a gravitational field and the fields of the sources are considered. In the first case, the singularity problem may be solved by constructing a Lagrangian that is regular in the vicinity of the topological transition. For gravitational-field sources this method is inapplicable, and therefore it is necessary either to use a mechanism analogous to the mechanism of spontaneous symmetry violation or to introduce additional boundary conditions which ensure regularity of the Lagrangian and the field equations.
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Konstantinov, M.Y. Singularities in the classical theory of topological transitions. Soviet Physics Journal 31, 982–985 (1988). https://doi.org/10.1007/BF01101166
- Boundary Condition
- Field Equation
- Classical Theory
- Gravitational Field
- Singularity Problem