Hilbert space representation of the minimal length uncertainty relation.
TL;DR: The quantum mechanical structure which underlies the generalized uncertainty relation which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements is studied.
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Abstract: The existence of a minimal observable length has long been suggested in quantum gravity as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation. DAMTP/94-105, hep-th/9412167, and Phys.Rev.D52:1108 (1995)
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References
Can spacetime be probed below the string size
TL;DR: In this paper, it was shown that if the energy is not so extreme to cause a gravitational instability and when the scattering angle approaches some critical value from below, the distance starts increasing, thus departing from the usual position-momentum uncertainty relation, and in no instance is the resolution smaller than the string length.
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Spacetime quantization induced by classical gravity
TL;DR: In this article, the authors propose spacetime uncertainty relations motivated by Heisenberg's uncertainty principle and by Einstein's theory of classical gravity, which is described by a non-commutative algebra whose commutation relations do imply our uncertainty relations.
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Minimum physical length and the generalized uncertainty principle in string theory
TL;DR: In this article, a possible definition of path integrals for string theory is studied, based on a discretized version of Polyakov's generating functional, and the finite resolution of string theory, as opposed to the infinite resolution in particle theory, clearly emerges from a renormalization group type analysis.
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The algebraic structure of the generalized uncertainty principle
TL;DR: In this article, it was shown that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity.
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