The problem of time and gauge invariance in the quantization of cosmological models. I. Canonical quantization methods

The paper is the first of two parts of a work reviewing some approaches to the problem of time in quantum cosmology, which were put forward last decade, and which demonstrated their relation to the problems of reparametrization and gauge invariance of quantum gravity. In the present part we remind basic features of quantum geometrodynamics and minisuperspace cosmological models, and discuss fundamental problems of the Wheeler - DeWitt theory. Various attempts to find a solution to the problem of time are considered in the framework of the canonical approach. Possible solutions to the problem are investigated making use of minisuperspace models, that is, systems with a finite number of degrees of freedom. At the same time, in the last section of the paper we expand our consideration beyond the minisuperspace approximation and briefly review promising ideas by Brown and Kuchar, who propose that dust interacting only gravitationally can be used for time measuring, and the unitary approach by Barvinsky and collaborators. The latter approach admits both the canonical and path integral formulations and anticipates the consideration of recent developments in the path integral approach in the second part of our work.Comment: 16 pages, to be published in Grav. Cosmo

Comment on the choice of time in a two-component formulation of the Wheeler--DeWitt equation

The two-component formalism in quantum cosmology is revisited with a particular emphasis on the identification of time. Its relation with the appearance of imaginary eigenvalues is established. It is explicitly shown how a good choice of the global time prevents this peculiarity.Comment: 8 pages; version accepted for publication in Int. J. Mod. Phys.

Wiggly Strings in Linearized Brans-Dicke Gravity

The metric around a wiggly cosmic string is calculated in the linear approximation of Brans-Dicke theory of gravitation. The equations of motion for relativistic and non-relativistic particles in this metric are obtained. Light propagation is also studied and it is shown that photon trajectories can be bounded.Comment: 10 pages, LaTeX, added reference

Time boundary terms and Dirac constraints

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.Comment: 12 page

Defect Detection System for Smartphone Front Camera Based on Improved Template Matching Algorithm

Automatic defect detection plays crucial role in resilient manufacturing in terms of product quality and cost effectiveness. With reference to the smartphone front cameras production process, the most recurrent defects can be classified into no hole, inner hole burr, outer circle damage, hole deformation, outer circle fracture and hole position offset. Due to the fast production lines and the defects micro size, Sampling-based methods has huge uncertainty and limitation, and Machine learning-based methods are characterised by low efficiency. To tackle these issues, this paper proposes a machine vision-based detection methods of smartphone front camera based on a multi-step template matching algorithm to reduce the computational effort. Specifically, in order to improve the algorithm efficiency, the images of the smartphone front cameras, acquired using industrial image acquisition devices are pre-processed by performing Hough circle and line transformations respectively, then locate the exact defect area as a region of interest (ROI). Finally, a multi-step template matching algorithm is used to detect and classify a number of common defects. Experimental results show an excellent suitability of the proposed system in detecting front camera surface defects. A benchmarking with other available technologies highlights how the proposed system yields an improvement in the detection speed by 46%, along with an improvement in the detection accuracy by 9%. The successful industrial implementation is discussed with reference to the integration into an automatic defect detection system in a smartphone front camera manufacturing context

Adiabatic renormalization in theories with modified dispersion relations

We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale $M_C$. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may contain finite trans-Planckian corrections even in the limit $M_C\to\infty$.Comment: Typos corrected; to appear in the Proceedings of IRGAC 06, Journal of Physics

Stability of Chaplygin gas thin-shell wormholes

In this paper we construct spherical thin-shell wormholes supported by a Chaplygin gas. For a rather general class of geometries we introduce a new approach for the stability analysis of static solutions under perturbations preserving the symmetry. We apply this to wormholes constructed from Schwarzschild, Schwarzschild-de Sitter, Schwarzschild-anti de Sitter and Reissner-Nordstrom metrics. In the last two cases, we find that there are values of the parameters for which stable static solutions exist.Comment: 14 pages, 5 figures; v2: minor changes and new references added. Accepted for publication in Physical Review