Related papers: Minimal Length Uncertainty Relation and gravitatio…
The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric…
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…
In this paper, we study the effect of the minimal length on neutrino oscillation in a static magnetic field. In the framework of the generalized uncertainty principle, we reformulate the Hamiltonian for a relativistic neutrino moving in a…
Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is usually…
A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative…
We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and Anti de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory,…
Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…
A Heisenberg uncertainty relation is derived for spatially-gated electric and magnetic field fluctuations. The uncertainty increases for small gating sizes which implies that in confined spaces the quantum nature of the electromagnetic…
This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General…
Many theories that attempt to formulate a quantum description of gravity suggest the existence of a fundamental minimum length scale. A popular method for incorporating this minimum length is through a modification of the Heisenberg…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first…
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be…
It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on…
We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize…
Quantum gravity effects modify the Heisenberg's uncertainty principle to a generalized uncertainty principle (GUP). Earlier work showed that the GUP-induced corrections to the Schr\"odinger equation, when applied to a non-relativistic…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far…
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
After picking out what may seem more realistic minimal gravitational deformation of quantum mechanics, we study its back reaction on gravity. The large distance behaviour of Newtonian potential coincides with the result obtained by using of…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…