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Studies in string theory and quantum gravity suggest the existence of a finite lower limit $Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example geometry is studied in detail.
Modifications of Heisenbergs uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change in the quan
Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.
The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements (COM microscope) it is shown that the spacetimes of Quantum Einstein Gravi
In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop q
In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relation $[X,P]=ihbarleft(1+beta P^2right)$ where $beta$ is the deformation parameter. Since the validity of the uncertainty