139 research outputs found
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
Higgs Scalar-Tensor Theory for Gravity and the Flat Rotation Curves of Spiral Galaxies
The scalar-tensor theory of gravity with the Higgs field as scalar field is
presented. For central symmetry it reproduces the empirically measured flat
rotation curves of galaxies. We approximate the galaxy by a polytropic gas
sphere with the polytropic index and a massive core.Comment: 17 pages, 12 figure
Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach
We investigate variations of the Zitterbewegung frequency of electron due to
an external static and uniform magnetic field employing the expectation value
quantum approach, and compare our results with the classical model of spinning
particles. We demonstrate that these two so far compatible approaches are not
in agreement in the presence of an external uniform static magnetic field, in
which the classical approach breaks the usual symmetry of free particles and
antiparticles states, i.e. it leads to CP violation. Hence, regarding the
Zitterbewegung frequency of electron, the classical approach in the presence of
an external magnetic field is unlikely to correctly describe the spin of
electron, while the quantum approach does, as expected. We also show that the
results obtained via the expectation value are in close agreement with the
quantum approach of the Heisenberg picture derived in the literature. However,
the method we use is capable of being compared with the classical approach
regarding the spin aspects. The classical interpretation of spin produced by
the altered Zitterbewegung frequency, in the presence of an external magnetic
field, are discussed.Comment: 16 pages, no figure
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Zweidimensionale Tragflächentheorie im Überschallgebiet
The plane problem of the vibrating airfoil in supersonic flow is dealt with and solved within the scope of a linearized theory by the method of the acceleration potential
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Über das Schallfeld einer gleichförmig-translatorisch bewegten punkförmigen Schallquelle
A rigorous analysis presented of the excitation of sound by point sources moving in uniform translatory motion at subsonic or supersonic velocities through a two- or three-dimensional medium at rest. The construction of surfaces of constant phase is based upon Huyghens' principle in such a manner that the propagation in the medium at rest of the elementary waves emanating from the sound source is independent of the momentary state of motion of the sound source. Hence, characteristic traits of the sound propagation may be understood even on the basis of simple geometric constructions
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