Topologie v teorii relativity

• Thesis title in Czech: Topologie v teorii relativity
• Thesis title in English: Topology in the Theory of Relativity
• Academic year of topic announcement: 2007/2008
• Thesis type: Bachelor's thesis
• Thesis language: čeština
• Department: Institute of Theoretical Physics (32-UTF)
• Supervisor: doc. RNDr. Otakar Svítek, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 13.11.2007
• Date of assignment: 13.11.2007
• Date and time of defence: 23.06.2009 00:00
• Date of electronic submission: 23.06.2009
• Date of proceeded defence: 23.06.2009
• Opponents: doc. RNDr. Martin Žofka, Ph.D.

Guidelines

Vypracovat přehled lokálních topologií v Minkowského prostoročasu, popsat jejich podstatné vlastnosti. Podrobněji rozebrat zejména takzvanou P-topologii (Path topology). Případně problematiku rozšířít i do Obecné teorie relativity.

References

1) G. L. Naber: The Geometry of Minkowski Spacetime, Springer-Verlag 1992
2) E. C. Zeeman: Causality Implies the Lorentz Group, J. Math. Phys. 5, Issue 4, pp. 490-493 (1964)
3) S. W. Hawking, A. R. King and P. J. McCarthy : A new topology for curved space–time which incorporates the causal, differential, and conformal structures, J. Math. Phys. 17, Issue 2, pp. 174-181 (1976)
4) Do-Hyung Kim: The path topology and the causal completion, J. Math. Phys. 47, 072503 (2006)

Preliminary scope of work

Ve Speciální teorii relativity se standardně uvažuje Euklidovská topologie, ovšem ta není z fyzikálního hlediska nikterak přirozená. Naopak takzvaná P-topologie přirozeným způsobem vede ke konformní Poincarého grupě.

Preliminary scope of work in English

In the Special Theory of Relativity the Euclidean topology is usually considered but it is not natural from the physical point of view. On the contrary, the so called P-topology naturally implies the conformal Poincaré group.