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Different candidates of quantum gravity proposal such as string theory, noncommutative geometry, loop quantum gravity and doubly special relativity, all predict the existence of a minimum observable length and/or a maximal momentum which…
A modification to the time-energy uncertainty relation in quantum gravity has been interpreted as increasing the duration of fluctuations producing virtual black holes with masses greater than the Planck mass. I point out that such virtual…
New collective coordinates, related to the field at the `center' of the monopoles, are proposed. A systematic computation of the infrared properties of 2+1- and 3+1- dimensional Yang-Mills theory is now possible and is related to solutions…
We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…
We study the short distance behaviour of euclidean quantum gravity in the light of Weinberg's asymptotic safety scenario. Implications of a non-trivial ultraviolet fixed point are reviewed. Based on an optimised renormalisation group, we…
We compute the ultraviolet divergences in the self-dual Yang-Mills theory, both in the purely perturbative (zero instanton charge) and topologically non-trivial sectors. It is shown in particular that the instanton measure is precisely the…
The dual superconductivity is a promising mechanism for quark confinement. We have presented a new formulation of the Yang-Mills theory on the lattice that enables us to change the original non-Abelian gauge field into the new field…
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…
This work presents physical consequences of our theory of induced gravity (Ref.1) regarding: 1) the requirement to consider shape and materials properties when calculating graviton cross section collision area; 2) use of Special Relativity;…
In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory (QFT) incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
A non-perturbative and mathematically rigorous quantum Yang-Mills theory on 4-dimensional Minkowski spacetime is set up in the functional framework of a complex nuclear Kree-Gelfand triple. It involves a symbolic calculus of operators with…
We briefly review some results in the theory of quantum $W_3$ gravity in the chiral gauge. We compare them with similar results in the analogous but simpler cases of $d=2$ induced gauge theories and $d=2$ induced gravity.
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude…
Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the…
Recently much work has been done in lowering the Planck threshold of quantum gravitational effects (sub-millimeter dimension(s), Horava-Witten fifth dimension, strings or branes low energy effects, etc.). Working in the framework of 4-dim…
A rectangular Wilson loop with sides parallel to space and time directions is perturbatively evaluated in two light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions, with ``instantaneous'' and ``causal'' interactions between…
We construct a unified covariant derivative that contains the sum of an affine connection and a Yang-Mills field. With it we construct a lagrangian that is invariant both under diffeomorphisms and Yang-Mills gauge transformations. We assume…
In the framework of linearized quantum gravity, we investigate the quantum gravitational interaction induced by the gravitodiamagnetic coupling of two massive objects to vacuum fluctuations of the gravitational field. Starting from the…
Here we discuss the ultraviolet and infrared aspects of the noncommutative counterpart of QED, which is called as noncommutative QED, as well as some infrared dynamics of noncommutative Yang-Mills (NCYM) theory. First we demonstrate that…