相关论文: Generic composition of boosts: an elementary deriv…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
The non-bijective version of Wigner's theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit…
In the light-front form of field theory, boost invariance is a manifest symmetry. On the downside, parity and rotational invariance are not manifest, leaving the possibility that approximations or incorrect renormalization might lead to…
We give a brief overview of a non-Lagrangian approach to field theory based on a generalization of the Kerr-Penrose theorem and algebraic twistor equations. Explicit algorithms for obtaining the set of fundamental (Maxwell, SL(2,…
In this paper in a framework of classical electrodynamics, we re-derived in a simple way the formula for the light scattering by moving particle with arbitrary angle of collision.
The simple reflection of a light beam of finite transverse extent from a homogenous interface gives rise to a surprisingly large number of subtle shifts and deflections which can be seen as diffractive corrections to the laws of geometrical…
The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total…
We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We…
Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux…
See math-ph/0205036 for an expanded version.
We derive simple formulas connecting the generalized Wigner functions for $s$-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
In this work we analyze the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin-$\frac{1}{2}$ particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner…
We study a simple generalization of the rotation (or circular shift) of the binary sequences. In particular, we show each orbit of this generalized rotation has a certain statistical symmetry. This generalized rotation naturally arises when…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…