12 citations · 28 across the 8 of their papers we have counts for
9 papers
Extended geometry and kinematics induced by biquaternionic and twistor structures
Vladimir V. Kassandrov, Nina V. Markova
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and re…
New symmetries, conserved quantities and gauge nature of a free Dirac field
Vladimir V. Kassandrov, Nina V. Markova
We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein-Gordon equation (KGE). We demonst…
Conservative relativistic algebrodynamics induced on an implicitly defined worldline
Abdel Challa, Vladimir V. Kassandrov, Nina V. Markova
In the framework of the Stueckelberg-Wheeler-Feynman concept of a ``one-electron Universe'' we consider a worldline implicitly defined by a system of algebraic (precisely, polynomi…
Relativistic generalization of the Schrodinger-Newton model for the wavefunction reduction
Vladimir V. Kassandrov, Nina V. Markova
We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of the Schrodinger…
Twistor structures and boost-invariant solutions to field equations
Vladimir V. Kassandrov, Joseph A. Rizcallah, Nina V. Markova
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…
Three kinds of particles on a single rationally parameterized worldline
Vladimir V. Kassandrov, Nina V. Markova
We consider the light cone (`retardation') equation (LCE) of an inertially moving observer and a single worldline parameterized by arbitrary rational functions. Then a set of appar…
Collective Lorentz invariant dynamics on a single "polynomial" worldline
Vladimir V. Kassandrov, Ildus Sh. Khasanov, Nina V. Markova
Consider a worldline of a pointlike particle parametrized by polynomial functions, together with the light cone ("retardation") equation of an inertially moving observer. Then a se…
Algebraic dynamics on a single worldline: Vieta formulas and conservation laws
V. V. Kassandrov, I. Sh. Khasanov, N. V. Markova
In development of the old conjecture of Stuckelberg, Wheeler and Feynman on the so-called "one electron Universe", we elaborate a purely algebraic construction of an ensemble of id…
On the model of a classical relativistic particle of constant and universal mass and spin
V. Kassandrov, N. Markova, G. Schaefer +1
The deformation of the classical action for a free relativistic particle recently suggested by A. Staruszkiewicz gives rise to a spin structure which constrains the values of the i…