Related papers: Minimal Length Uncertainty Relation and Ultraviole…
We study a framework where the hypothesis of a minimum length in space-time is complemented with the notion of reference frame invariance. It turns out natural to interpret the action of the obtained reference frame transformations in the…
For $0<\gamma<2$ and $\delta>0$, we consider the Liouville graph distance, which is the minimal number of Euclidean balls of $\gamma$-Liouville quantum gravity measure at most $\delta$ whose union contains a continuous path between two…
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…
The set of space-time short-distance structures which can be described through linear operators is limited to a few basic cases. These are continua, lattices and a further short-distance structure which implies an ultraviolet cut-off. Under…
If the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator, perturbative quantum gravity corrections can be partially resummed into a series…
I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely…
Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P is the Planck length. Their idea is roughly…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically…
A recently conjectured relashionship between UV and IR cutoffs in an effective field theory without quantum gravity is generalized in the presence of large extra dimensions. Estimates for the corrections to the usual calculation of…
Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009 the observation of a short gamma ray burst…
To achieve a maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. This optimization procedure is applied to the scalar theory in $D+1$ dimensions…
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of…
Recently it was demonstrated that the theoretical predictions for the Planck scale space-time fluctuations derived by the simultaneous consideration of quantum mechanics and general relativity fail by many orders of magnitude against the…
Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. In this paper, we examine these obstructions…
Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of…
We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude…
The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
I review the current status of FDR, the recently introduced Four-Dimensional Regularization/Renormalization approach to ultraviolet divergences in Quantum Field Theory. FDR also regulates infrared and collinear infinities in the…