NDLI: Structure of Malicious Singularities

Content Provider	Springer Nature Link
Author	Heller, Michael Odrzygóźdź, Zdzislaw Pysiak, Leszek Sasin, Wieslaw
Copyright Year	2003
Abstract	In this paper, we investigate relativistic spacetimes, together with their singular boundaries (including the strongest singularities of the Big Bang type, called malicious singularities), as noncommutative spaces. Such a space is defined by a noncommutative algebra on the transformation groupoid Γ = Ē × G, where Ē is the total space of the frame bundle over spacetime with its singular boundary, and G is its structural group. We show that there exists the bijective correspondence between unitary representations of the groupoid Γ and the systems of imprimitivity of the group G. This allows us to apply the Mackey theorem to this case, and deduce from it some information concerning singular fibers of the groupoid Γ. At regular points the group representation, which is a part of the corresponding system of imprimitivity, does not have discrete components, whereas at the malicious singularity such a group representation can be a single representation (in particular, an irreducible one) or a direct sum of such representations. A subgroup K ⊂ G, from which—according to the Mackey theorem—the representation is induced to the whole of G, can be regarded as measuring the “richness” of the singularity structure. In this sense, the structure of malicious singularities is richer than those of milder ones.
Starting Page	427
Ending Page	441
Page Count	15
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	42
Issue Number	3
e-ISSN	15729575
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2003-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Physics Quantum Physics Mathematical and Computational Physics Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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