相关论文: Generic composition of boosts: an elementary deriv…

Whatever dark matter is, it must be one irreducible unitary representation of the extended Lorentz group or another. We here develop a formalism of mass dimension one fermions and bosons of spin one half, and show that they provide natural…

A derivation is given of the Boltzmann-Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of…

Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…

A special case of the relativistic Doppler effect, which occurs when light reflects from a moving mirror, is discussed. The classic formula for the Doppler shift is derived in a fully non-relativistic fashion using basic facts from…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification…

The ordered addition of two Lorentz boosts is normally shown to result in a boost by utilizing concepts from group theory and non-Euclidian geometry. We present a method for achieving this addition by performing a sequence of spatial…

Wigner's particle classification provides for "continuous spin" representations of the Poincar\'e group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by use of "Wigner…

We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…

We report the simplest possible form to compute rotations around arbitrary axis and boosts in arbitrary directions for 4-vectors (space-time points, energy-momentum) and bi-vectors (electric and magnetic field vectors) by symplectic…

We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two…

In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number…

The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…

Based on superfluid behavior of a (boson) dark matter as the light itself, a unified model for dark matter and quintessence is proposed. Inspired by (O'Dell et al. 2000) which in an exciting study showed that particular configurations of…

An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…

Fundamentals of the local smooth loops due to Sabinin are concisely outlined together with the corresponding infinitesimal objects, so-called \nu-hyperalgebras, and the analogue of the Lie groups theory. We apply here this theory to to…

An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression…

The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the…

In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…

According to the theory of general relativity, masses deflect light in a way similar to convex glass lenses. This gravitational lensing effect is astigmatic, giving rise to image distortions. These distortions allow to quantify cosmic…