31. Piotr T. Chru¶ciel, Christa R. Ölz, Sebastian J. Szybka
Space-time diagrammatics
Phys. Rev. D: Part. Fields , vol. 86, p. 124041 (2012).
[abstract] [preprint] [journal] [download] |
Abstract:
We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti) de Sitter family, with or without cosmological constant, and the Emparan-Reall black rings. |
32. Andrzej Sitarz
Causality and Noncommutativity
Conference "The Causal Universe", vol. xxx, pp. xxx-xxx (2012).
[abstract] [download] |
Abstract:
Noncommutative Geometry o ers a modern mathematical approach to the formulation of physical models, which comprise gravity and gauge theories. We review its basic ideas, applications to models with Lorentzian geometry and challenges it poses to our understanding of causality. |
33. A. Sitarz, A. Zaj±c
Spectral action for scalar perturbations of Dirac operators
Lett. Math. Phys., vol. 98, pp. 333-348 (2011).
[abstract] [preprint] [journal] [download] |
Abstract:
We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey–de Witt coefficients and make explicit calculations for the case of n-spheres with a completely symmetric Dirac. In the special case of dimension 3, when such perturbation corresponds to the completely antisymmetric torsion, we carry out the noncommutative calculation following Chamseddine and Connes (J Geom Phys 57:121, 2006) and study the case of SU q (2). |
34. B. Iochum, T. Masson, T. Schücker, A. Sitarz
Compact kappa-deformation and spectral triples
Rep. Math. Phys., vol. 68, pp. 37-64 (2011).
[abstract] [journal] |
Abstract:
We construct discrete versions of κ-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical system of the underlying discrete groups (which include some Baumslag–Solitar groups) is heavily used in order to construct finitely summable spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation. The dimension of these spectral triples is unrelated to the number of coordinates defining the κ-deformed Minkowski spaces. |
35. B. Iochum, T. Masson, T. Schücker, A. Sitarz
Kappa-deformation and Spectral Triples
Acta Phys. Polon. Supp., vol. 4, p. 305 (2011).
[abstract] [preprint] [journal] [download] |
Abstract:
The aim of the paper is to answer the following question: does kappa -deformation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of kappa -Minkowski deformation via C*-algebras of groups. The dynamical system of the underlying groups (including some Baumslag–Solitar groups) is used in order to construct finitely summable spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation. |
36. Michael Heller, Leszek Pysiak and Wies³aw Sasin
Fundamental Problems in the Unification of Physics
Foundations of Physics, vol. 41, pp. 905-918 (2011).
[abstract] [preprint] [journal] [download] |
Abstract:
We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues. |
