Related papers: Space and time transformations with a minimal leng…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We propose the idea that time evolution of quantum systems is driven by work. The formalism presented here falls within the scope of a recently proposed theory of gravitating quantum matter where extractible work, and not energy, is…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the…
Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…
Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
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…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
We consider the scenario of a fluctuating spacetime due to a deformed commutation relation with a fluctuating deformation parameter, or to a fluctuating metric tensor. By computing the resulting dynamics and averaging over these…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…
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…
We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno…