Generalized uncertainty principle from quantum geometry. (English) Zbl 0981.83021

Capozziello, S.; Lambiase, G.; Scarpetta, G.

Int. J. Theor. Phys. 39, No. 1, 15-22 (2000).

The generalized uncertainty principle of string theory \(\Delta x\geq \hbar /2\Delta p+\alpha c^{-3}G\Delta p\) (where \(G\) is the Newton constant and \( \alpha \) is a constant) is derived in the framework of quantum geometry by taking into account the existence of an upper limit on the acceleration of massive particles. Its formulation is based on the fact that the position and momentum operators are represented as covariant derivatives with an appropriate connection in the eight-dimensional manifold and the quantization is geometrically interpreted as curvature of phase space. A consequence of this geometric approach is the existence of maximal acceleration \({\mathcal A}\) defined as the upper limit to the proper acceleration experienced by massive particles along their worldlines, which can be interpreted as mass dependent, \({\mathcal A}_{m}=2mc^{3}/\hbar \) (\(m\) is the mass of particle), or as a universal constant, \({\mathcal A} =m_{P}c^{3}/\hbar \) (\(m_{P}\) is the Planck mass). Since the regime of validity of the generalized uncertainty principle is at Planck scales, in order to derive it from quantum geometry, the maximal acceleration depending on the Planck mass is considered.

Reviewer: Steven Duplij (Kharkov)

MSC:

83C45	Quantization of the gravitational field
83E05	Geometrodynamics and the holographic principle
83E15	Kaluza-Klein and other higher-dimensional theories

Keywords:

generalized uncertainty principle; eight-dimensional space-time; maximal acceleration; Hilbert space; quantum fluctuation