Generalized uncertainty principle, extra dimensions and holography. (English) Zbl 1048.83009

Summary: We consider uncertainty principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such generalized uncertainty principles in \(4+n\) dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.


83C45 Quantization of the gravitational field
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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