Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography

Details Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography

2001-03-14

arxiv.org/abs/hep-th/0103107v2

JHEP 0205 (2002) 033

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, harvmac. v2: typos corrected and some changes made

Scientific paper

10.1088/1126-6708/2002/05/033

Unlike noncommutative space, when space and time are noncommutative, it seems necessary to modify the usual scheme of quantum mechanics. We propose in this paper a simple generalization of the time evolution equation in quantum mechanics to incorporate the feature of a noncommutative spacetime. This equation is much more constraining than the usual Schr\"odinger equation in that the spatial dimension noncommuting with time is effectively reduced to a point in low energy. We thus call the new evolution equation the spacetime bootstrap equation, the dimensional reduction called for by this evolution seems close to what is required by the holographic principle. We will discuss several examples to demonstrate this point.

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