Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-11-16
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
ReVTeX4, 13 pages, 2 figures,major corrections in the definition of the singular form, the trace and the complex structure
Scientific paper
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor understanding of the geometrical character of quantum mechanics. In Einstein's theory gravitation is expressed by geometry of space-time, and the solutions of the field equation are invariant w.r.t. a certain equivalence class of reference frames. This class can be characterized by the differential structure of space-time. We will show that matter is the transition between reference frames that belong to different differential structures, that the set of transitions of the differential structure is given by a Temperley-Lieb algebra which is extensible to a $C^{*}$-algebra comprising the field operator algebra of quantum mechanics and that the state space of quantum mechanics is the linear space of the differential structures. Furthermore we are able to explain the appearance of the complex numbers in quantum theory. The strong relation to Loop Quantum Gravity is discussed in conclusion.
Asselmeyer-Maluga Torsten
Rose' Helge
No associations
LandOfFree
Differential Structures - the Geometrization of Quantum Mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Differential Structures - the Geometrization of Quantum Mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differential Structures - the Geometrization of Quantum Mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-581035