Recent results on UV-regularisation through UV-modified uncertainty relations

1997/11/28 by A. Kempf, Kempf, A.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9711204

4 pages, LaTeX, to appear in Proceedings 5th Wigner Symposium, Vienna, Aug 97

arxiv created 1997/11/28 · arxiv updated 2009/11/30

Abstract

Assume that in a fundamental theory of quantum gravity spatial information is encoded through elements x_i of an associative, complex and possibly noncommutative algebra in which the involution acts as x^*_i = x_i. Without further assumptions it can be shown that such x_i can describe only three different types of short distance structures: I. a lattice, II. a continuum or III. a finite lower bound on the uncertainty in positions, as e.g. described in a stringy uncertainty relation. All other cases are mixtures of the three. We briefly review recent results on the case III short distance structure, in particular its ultraviolet regularity and a possible new mechanism that turns the external degrees of freedom lost through the UV-cutoff into internal degrees of freedom.

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