Covariant quantizations in plane and curved spaces

We present covariant quantization rules for nonsingular finite dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian coordinates. This family is parametrized by a function $\omega(\theta)$, $\theta\in\left( 1,0\right)$, which describes an ambiguity of the quantization. We generalize this construction presenting covariant quantizations of theories with flat configuration spaces but already with arbitrary curvilinear coordinates. Then we construct a so-called minimal family of covariant quantizations for theories with curved configuration spaces. This family of quantizations is parametrized by the same function $\omega \left( \theta \right)$. Finally, we describe a more wide family of covariant quantizations in curved spaces. This family is already parametrized by two functions, the previous one $\omega(\theta)$ and by an additional function $\Theta \left( x,\xi \right)$. The above mentioned minimal family is a part at $\Theta =1$ of the wide family of quantizations. We study constructed quantizations in detail, proving their consistency and covariance. As a physical application, we consider a quantization of a non-relativistic particle moving in a curved space, discussing the problem of a quantum potential. Applying the covariant quantizations in flat spaces to an old problem of constructing quantum Hamiltonian in Polar coordinates, we directly obtain a correct result.Comment: 38 pages, 2 figures, version published in The European Physical Journal

Covariant quantizations in plane and curved spaces

We present covariant quantization rules for nonsingular finite dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian coordinates. This family is parametrized by a function ω(θ), θ∈(1,0), which describes an ambiguity of the quantization. We generalize this construction presenting covariant quantizations of theories with flat configuration spaces but already with arbitrary curvilinear coordinates. Then we construct a so-called minimal family of covariant quantizations for theories with curved configuration spaces. This family of quantizations is parametrized by the same function ω(θ). Finally, we describe a more wide family of covariant quantizations in curved spaces. This family is already parametrized by two functions, the previous one ω(θ) and by an additional function Θ(x,ξ). The above mentioned minimal family is a part at Θ=1 of the wide family of quantizations. We study constructed quantizations in detail, proving their consistency and covariance. As a physical application, we consider a quantization of a non-relativistic particle moving in a curved space, discussing the problem of a quantum potential. Applying the covariant quantizations in flat spaces to an old problem of constructing quantum Hamiltonian in Polar coordinates, we directly obtain a correct result

Evaluating Focal Stack with Compressive Sensing

Compressive sensing (CS) has demonstrated the ability in the field of signal and image processing to reconstruct signals from fewer samples than prescribed by the Shannon-Nyquist algorithm. In this paper, we evaluate the results of the application of a compressive sensing based fusion algorithm to a Focal Stack (FS) set of images of different focal planes to produce a single All In-Focus Image. This model, tests l1 -norm optimization to reconstruct a set of images, called a Focal Stack to reproduce the scene with all focused points. This method can be used with any Epsilon Photography algorithm, such as Lucky Imaging, Multi-Image panorama stitching, or Confocal Stereo. The images are aligned and blocked first for faster processing time and better accuracy. We evaluate our results by calculating the correlation of each block with the corresponding focus plane. We also discuss the shortcomings of this simulation as well as the potential improvements on this algorithm

GTKDynamo: a PyMOL plug-in for QC/MM hybrid potential simulations.

International audienceHybrid quantum chemical/molecular mechanical (QCMM) potentials are very powerful tools for molecular simulation. They are especially useful for studying processes in condensed phase systems, such as chemical reactions that involve a relatively localized change in electronic structure and where the surrounding environment contributes to these changes but can be represented with more computationally efficient functional forms. Despite their utility, however, these potentials are not always straightforward to apply since the extent of significant electronic structure changes occurring in the condensed phase process may not be intuitively obvious. To facilitate their use, we have developed an open-source graphical plug-in, GTKDynamo that links the PyMOL visualization program and the pDynamo QC/MM simulation library. This article describes the implementation of GTKDynamo and its capabilities and illustrates its application to QC/MM simulations