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It is proposed a natural and consistent division of the momentum of electromagnetic waves in linear, non-dispersive and non-absorptive dielectric and magnetic media into material and electromagnetic parts. The material part is calculated…
Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a…
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…
Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schr\"odinger cat states would macroscopically violate the standard…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $\delta$ and velocity-divergence fields $\theta$. In particular, we derive an evolution equation for the one-point…
We study the effects of a barely perceivable violation of Lorentz invariance on results computed using a relativistic constituent quark model wave function. The model nucleon wave function of Gross {\it et al.} is constructed such thatthere…
A model is presented allowing calculation of energy and matter distribution in the Universe after expansion from singularity without introduction of expansion energy. Beginning with Fick's law of diffusion, we solve the Bessel function for…
Dark matter in the cosmological concordance model is parameterised by a single number, describing the covariantly conserved energy density of a non-relativistic fluid. Here we test this assumption in a model-independent and conservative way…
We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light. In order to perform this expansion it…
We seek to introduce a mathematical method to derive the relativistic wave equations for two-particle system. According to this method, if we define stationary wave functions as special solutions like…
The standard quantum mechanics assumes Schr\"odinger equation for regular evolution and wave function collapse for measurement. As shown in this paper, only particular collapse equation can continuously transition to Schr\"odinge equation.…
The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy wave function in much the same way that one derives QFT for electrons, that is, by quantization…
Evolution of the large scale structure of the Universe is described by galaxy bias and the growth rate function of the matter density contrast. The behavior of the growth rate function, in general, depends on the types of dark energy or…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We have obtained a generalization of the hydrodynamic theory of vacuum in the context of general relativity. While retaining the Lagrangian character of general relativity, the new theory provides a natural alternative to the view that the…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…