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In contrast to the 3D case, different approaches for deriving thegravitational corrections to the Heisenberg uncertainty relation do not lead tothe unique result whereas additional spatial dimensions are present in thetheory. We suggest to take logarithmic corrections to the black hole entropy,which has recently been proved both in string theory and loop quantum gravityto persist in presence of additional spatial dimensions, as a point of entryfor identifying the modified Heisenberg-Weyl algebra. We then use a particularHilbert space representation for such a quantum mechanics to construct thecorrespondingly modified field theory and address some phenomenological issuesfollowing from it. Some subtleties arising at the second quantization level areclearly pointed out. Solving the field operator to the first order indeformation parameter and defining the modified wave function for a freeparticle, we discuss the possible phenomenological implications for the blackhole evaporation. Putting aside modifications arising at the secondquantization level, we address the corrections to the gravitational potentialdue to modified propagator (back reaction on gravity) and see thatcorrespondingly modified Schwarzschild-Tangherlini space-time shows up thedisappearance of the horizon and vanishing of surface gravity when black holemass approaches the quantum gravity scale. This result points out to theexistence of zero-temperature black hole remnants.

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