Related papers: A cosmological viewpoint on the correspondence bet…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks,…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…
We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity, wherein an arbitrary function of the boundary term, namely $B$, is present in the action and in the other model a scalar field that is…
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
This paper presents a PDE-based approach to finding an optimal canonical basis with which to represent a nearly integrable Hamiltonian. The idea behind the method is to continuously deform the initial canonical basis in such a way that the…
We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology…
This work applies the principles of quantum cosmology to examine models incorporating a quintom field. Specifically, three distinct models are analyzed: a simplified toy model, a model featuring an exponential quintom potential, and one…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The…
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on…
A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved…
Different proposals for the wave function of the universe are analyzed, with an emphasis on various forms of the tunneling proposal. The issues discussed include the equivalence of the Lorentzian path integral and outgoing-wave proposals,…
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
We use a deformed differential structure to obtain a curved metric by a deformation quantization of the flat space-time. In particular, by setting the deformation parameters to be equal to physical constants we obtain the…
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…
Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…