Related papers: Exact path integrals on half-line in quantum cosmo…
A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
We consider minisuperspace models with two-derivative kinetic terms, assuming a flat target space and a closed Universe. We show that, upon canonical quantization of the Hamiltonian, only a restricted class of operator orderings is…
Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations. In the second…
In this work a loop quantum corrected model is obtained for spherically symmetric space-times in the vacuum. This effective model is derived by the use of the path integral method, previously employed in several models of Loop Quantum…
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…
Sharply peaked quantum states are conjectured to be conducive to the notion of a quantum-corrected spacetime. We investigate this conjecture for a flat-FLRW model with perfect fluid, where a generalized ordering scheme is considered for the…
The overcompleteness of the coherent states basis leads to a multiplicity of representations of Feynman's path integral. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. Two…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
We formulate a new quantum equivalence principle by which a path integral for a particle in a general metric-affine space is obtained from that in a flat space by a non-holonomic coordinate transformation. The new path integral is free of…
In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator. We study the initial singularity and the large volume limit against the ambiguities in the discretisation and the operator ordering within a homogeneous,…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…