相关论文: WKB approximation in deformed space with minimal l…
Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…
We introduce a method for calculating the joint spectra of functions which comprise a quantum integrable system under a deformation quantization star product. The main result involves a construction by formal power series in h-bar of…
Quantum fields exhibit non-trivial behaviours in curved space-times, especially around black holes or when a cosmological constant is added to the field equations. A new scheme, based on the Wentzel-Kramers-Brillouin (WKB) approximation is…
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to cosmological models in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in a flat minisuperspace. The de Sitter…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
Deformation quantization is applied to quantize gravitational systems coupled with matter. This quantization procedure is performed explicitly for quantum cosmology of these systems in a flat minisuper(phase)space. The procedure is employed…
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…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
A suitable deformation of the Hopf algebra of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational…
The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
We apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations.…
In this paper we present a Friedmann-Robertson-Walker cosmological model conformally coupled to a massive scalar field where the WKB approximation fails to reproduce the exact solution to the Wheeler-DeWitt equation for large Universes. The…
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
Studies in string theory and quantum gravity lead to the Generalized Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra.…
We present a new short-time approximation scheme for evaluation of decoherence. At low temperatures, the approximation is argued to apply at intermediate times as well. It then provides a tractable approach complementary to Markovian-type…
We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…
We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the…
The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated…