We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates. ∗email: [email protected]

We study the recent introduced dressed coordinates in the path-integral approach. We define these coordinates in the context of a harmonic oscillator linearly coupled to massless scalar field and, we show that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. We also generalize the sum rules established in a previous work.

The recent introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and, it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules establish...

geospatial information system (gis) has emerged as a very powerful tool for capturing, storing, analyzing, managing, and presenting data that is linked to location. the location information, which is usually obtained from existing maps or the global positioning systems (gps), refers to different coordinate and map projection systems. therefore, unification of the coordinate and mapping systems ...

We study the recent introduced dressed coordinates in the path-integral approach. We define these coordinates in the context of a harmonic oscillator linearly coupled to massless scalar field and, we show that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. We also generalize the sum rules established in a previous work.

The article discusses the problem of transformation in the form of the function f : R2 R2 as dependence between the coordinates [x, y] of the original system and the coordinates [X, Y] of the secondary system. The task of the transformation of [ , ] ( , ) X Y f x y technically understood as the transformation of a system of coordinates has been solved by means of the feed-forward neural network...

We identify an intermediate coordinate system situated between world coordinates and display coordinates, which exhibits unique features for lighting calculations and for clipping in homogeneous coordinates. Our key contribution is an algorithm for extracting such a coordinate system from a homogeneous viewing transformation that relates WC to DC. The algorithm is based on factoring the transfo...

Maxwell’s curl equations are formulated in curvilinear non-orthogonal coordinates in three dimensions in a manner that enables to preserve conventional Cartesian mesh for the finite-difference schemes by means of mere redefinition of the permittivity and permeability coefficients. It is highlighted that in the previous works on this subject (Ward and Pendry 1996 J. Modern Opt. 43 773; 1998 Phys...

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliub...