Abstract
We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of nonperturbative string theory.
Highlights
One of the unequivocal characteristics of string theory 1–3 is its possession of a fundamental lengt√h scale which determines the typical spacetime extension of a fundamental string
This is s α, where c/α is the string tension. Such a feature is to be expected of any candidate theory of quantum gravity, since gravity itself is characterized by the Planck length P
We focus our attention on how a minimal length can be introduced into quantum mechanics by modifying its algebraic structure 48–50
Summary
One of the unequivocal characteristics of string theory 1–3 is its possession of a fundamental lengt√h scale which determines the typical spacetime extension of a fundamental string. A natural question to ask is, whether the formalism of quantum theory can be deformed or extended in such a way as to consistently incorporate the minimal length. The starting point of our analysis is the minimal length uncertainty relation MLUR 51, 52 , δx ∼ δp α δp , 1.2 which is suggested by a resummed perturbation expansion of the string-string scattering amplitude in a flat spacetime background 53–56. This is essentially a Heisenberg microscope argument 57 in the S-matrix language 58–61 with fundamental strings used to probe fundamental strings.
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