Related papers: Invariant relativistic kinematics: Phase space tri…
We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon…
We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…
Several approaches to quantum gravity suggest that the standard description of spacetime as probed at low-energy, with four dimensions, is replaced in the Planckian regime by a spacetime with a spectral dimension of two. The implications…
We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are…
It is shown that general dilepton angular distribution (with parity violating terms taking into account) in vector particle decays can be described through a set of five SO(3) rotational-invariant observables. These observables are derived…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
A manifest covariant equilibrium statistical mechanics is constructed starting with a 8N dimensional extended phase space which is reduced to the 6N physical degrees of freedom using the Poincare-invariant constrained Hamiltonian dynamics…
We define a complex relativistic phase space which is the space $\mathbb{C}^4$ equipped with the Minkowski metric and with a geometric tri-product on it. The geometric tri-product is similar to the triple product of the bounded symmetric…
Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidence suggest that magnetized…
In this paper, we discuss duality about components of invariant variety of periodic points(IVPP) and fundamental domain of recurrence equation, and present an algorithm for the derivation of all components of IVPPs of any rational maps. It…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to…
Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a…