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

A. Kempf
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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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A. Kempf. 1997-11-28. Recent results on UV-regularisation through UV-modified uncertainty relations. https://arxiv.org/abs/hep-th/9711204

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