Related papers: Generalized Quantization Principle in Canonical Qu…
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…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology…
A Kantowski-Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called Generalized Uncertainty Principle (GUP), correspond to a modified commutation relation between…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
The finite and infinite square wells are potentials typically discussed in undergraduate quantum mechanics courses. In this paper, we discuss these potentials in the light of the recent studies of the modification of the Heisenberg…
We construct a quantum theory of free scalar field in 1+1 dimensions based on a `Generalized Uncertainty Principle'. Both canonical and path integral formalism are employed. Higher dimensional extension is easily performed in the path…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
We study the quantum cosmology of a quadratic $f(R)$ theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamics of the scalar field is induced. The classical equations of motion and the Weeler-deWitt…
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation…
The basic principles of the quantum mechanics in the K-field formalism are stated in the paper. The basic distinction of this theory arises from that the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic…