Related papers: Relativistic combination of non-collinear 3-veloci…
It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field…
It turns out that the standard application of the four-vector SR formalism does not include the concept of relative velocity. Only the absolute velocity is described by the four-vector, and even the Lorentz transformation parameters is…
We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in…
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L\'{e}vy index $\alpha $. The model applies to…
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…
In this article, we introduce the notion of Quaternion Boostlet Transform (QBT), a hypercomplex framework designed to unify the analysis of multi-component wavefields by merging the algebraic richness of quaternions with the relativistic,…
We argue that quaternions form a natural language for the description of quantum-mechanical wavefunctions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No…
We give an explicit algebraic description of finite Lorentz transformations of vectors in 10-dimensional Minkowski space by means of a parameterization in terms of the octonions. The possible utility of these results for superstring theory…
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…
In the framework based on the quasipotential method and relativistic quark model a new covariant expression for the heavy quark fragmentation amplitude to fragment into the pseudoscalar and vector S-wave heavy mesons is obtained. It…
We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions. Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees…
Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation.…
It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over…
A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
Some results about non-bijective quadratic transformations generalizing the Kustaanheimo-Stiefel and the Levi-Civita transformations are reviewed in \S 1. The three remaining sections are devoted to new results: \S 2 deals with the Lie…