# Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

In contrast to the 3D case, different approaches for deriving the gravitational corrections to the Heisenberg uncertainty relation do not lead to the unique result whereas additional spatial dimensions are present in the theory. We suggest to take logarithmic corrections to the black hole entropy, which has recently been proved both in string theory and loop quantum gravity to persist in presence of additional spatial dimensions, as a point of entry for identifying the modified Heisenberg-Weyl algebra. We then use a particular Hilbert space representation for such a quantum mechanics to construct the correspondingly modified field theory and address some phenomenological issues following from it. Some subtleties arising at the second quantization level are clearly pointed out. Solving the field operator to the first order in deformation parameter and defining the modified wave function for a free particle, we discuss the possible phenomenological implications for the black hole evaporation. Putting aside modifications arising at the second quantization level, we address the corrections to the gravitational potential due to modified propagator (back reaction on gravity) and see that correspondingly modified Schwarzschild-Tangherlini space-time shows up the disappearance of the horizon and vanishing of surface gravity when black hole mass approaches the quantum gravity scale. This result points out to the existence of zero-temperature black hole remnants.

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