Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Differential Structures  the Geometrization of Quantum Mechanics
 Online im WWW, 2005, 13 S. 

 Englisch 
 Bericht, Elektronische Publikation 
 Fraunhofer FIRST () 
Abstract
The usual quantization of a classical spacetime field does not touch the nongeometrical 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 spacetime, 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 spacetime. 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 TemperleyLieb 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.