Related papers: Unification of Spacetime Symmetries of Massive and…
The massive non-relativistic free particle in d-1 space dimensions has an action with a surprizing non-linearly realized SO(d,2) symmetry. This is the simplest example of a host of diverse one-time-physics systems with hidden SO(d,2)…
The relativistic two-component equation describing the free motion of particles with zero mass and spin 1/2, which is P- and T-non-invariant but C-invariant, is found. The representation of the Poincare group for zero mass and discrete spin…
The quark masses evaluated by the Particle Data Group are consistent with terms in a geometric progression of mass values descending from the Planck Mass. The common ratio of the sequence is 2/pi. The quarks occupy the 'principal' levels of…
We consider the scattering of massless particles coupled to an abelian gauge field in 2n-dimensional Minkowski spacetime. Weinberg's soft photon theorem is recast as Ward identities for infinitely many new nontrivial symmetries of the…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We predict that large moments $J$, placed into a crystal field with the cubic point symmetry group, differ by their spectrum and magnetic properties. E. g., properties of the odd-integer moments are different from those of the even-integer.…
A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or…
We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…
In this paper, we investigate the spacetime containing both small-scale structures (wiggles) and spatial dislocation, forming a wiggly cosmic dislocation. We study the combined effects of these features on the dynamics of massive and…
We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The general model of an arbitrary spin massive particle in any dimensional space-time is derived on the basis of Kirillov - Kostant - Souriau approach. Keywords: spinning particles, Poincar\'e group, orbit method, constrained dynamics,…
Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…
We represent sixteen-component values "sedeons", generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It…
It is shown that for a specific choice of a particular solution of the relativistic wave equation, it falls into the Helmholtz equation and the Klein -Gordon equation. In this case, the squares of the rest masses of the particle with the…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
The Standard Model plus gravitation is derived from general relativity with three dimensions of time. I claim that when the Lagrangian for general relativity is calculated using three dimensions of time, the unified field theory results. I…
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…
Strong repelling interactions between a few fermions or bosons confined in two-dimensional circular traps lead to particle localization and formation of quantum Wigner molecules (QWMs) possessing definite point-group space symmetries. These…
In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…