The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential features ofWigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the ...

Abstract. It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincaré group do not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear coordinates are used to describe the momentum generators within ...

Tunneling phenomenon is well recognized as one of the most important quantum mechanical effects from the dawn of quantum mechanics, and it actually plays crucial role in all branches of science from elementary particle physics to biology. In this work, we consider one of the basic phenomena: tunneling splitting in multi-dimensional double well potential and present a canonically invariant insta...

Abstract. It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincaré group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear coordinates are used to describe the momentum generators withi...

We consider massless elementary particles in a quantum theory based on a Galois field (GFQT). We previously showed that the theory has a new symmetry between particles and antiparticles, which has no analogue in the standard approach. We now prove that the symmetry is compatible with all operators describing massless particles. Consequently, massless elementary particles can have only the half-...

In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). We believe that the fact that this modification is consi...

It is easy to draw an intuitive parallel between the classical free electromagnetic field and its corresponding quantum, the photon-a spin-1 object. The situation with a massive particle such as an electron is less clear, as a real-world analog of the classical field whose quantum is the massive particle is not available. It is concluded that the fermion particle perspective provides the best a...

Large Hadron Collider (LHC) experiments this year have shown the existence of a new boson that resembles the Higgs boson. Although it is known that this particle has couplings to other particles that increase with their masses, the spin of the newly discovered boson is undetermined as of yet. The Higgs boson has been predicted to be a spin 0 particle. The LHC boson is not a spin 1 particle, sug...

It is shown that particle motion in a bent (straight) crystal is accompanied by particle spin rotation and oscillations that allows to measure the tensor electric polarizability of nuclei and elementary particles.