Quantization of Space and Time in 3 and in 4 Space-time Dimensions

Details Quantization of Space and Time in 3 and in 4 Space-time Dimensions Quantization of Space and Time in 3 and in 4 Space-time Dimensions

1996-08-16

arxiv.org/abs/gr-qc/9608037v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Lectures held at the NATO Advanced Study Institute on ``Quantum Fields and Quantum Space Time", Carg\`ese, July 22 -- August 3

Scientific paper

The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is demonstrated first in a model where particles behave as point defects in 2 space dimensions and 1 time, and then in the real world having 3+1 dimensions. The mechanisms in these two cases are quite different, but the outcomes are similar: space and time form a (non-cummutative) lattice. These notes are short since most of the material discussed in these lectures is based on two earlier papers by the same author (gr-qc/9601014 and gr-qc/9607022), but the exposition given in the end is new.

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