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Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
The existence of a fundamental scale is expected to be a key feature of quantum gravity. Many approaches take this property as a starting assumption. Here, instead, we take a less conventional viewpoint based on a critical inspection of…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
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…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
The Generalized Uncertainty Principle (GUP) extends the Heisenberg Uncertainty Principle (HUP) by suggesting a minimum observable scale that includes the effects of quantum gravity, which is supposed to potentially result in observable…
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of…
Using the Steiner-Weyl expansion formula for parallel manifolds and the so called gonihedric principle we find a large class of discrete integral invariants which are defined on simplicial manifolds of various dimensions. These integral…
The generalized uncertainty principle (GUP) is a modification of standard quantum mechanics due to Planck scale effects. The GUP has recently been used to improve the short distance behaviour of classical black hole spacetimes by invoking…
Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with…
We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of…
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…
An analysis of the Schwinger's action principle in Lagrangian quantum field theory is presented. A solution of a problem contained in it is proposed via a suitable definition of a derivative with respect to operator variables. This results…
A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…