51 research outputs found
Non-relativistic classical mechanics for spinning particles
We study the classical dynamics of non-relativistic particles endowed with
spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also
in the small momentum limit. We derive a generalized work-energy theorem which
suggests classical interpretations for tunnel effect and quantum potential
Helicity-0 spinning particles
We show that a self-consistent classical theory of the spin, based on a very
general Lagrangian extending the Newtonian dynamics, does predict the special
case of helicity-0 particles, which at the same time are endowed with nonzero
spin and zero intrinsic angular momentum.Comment: 9 page
Deriving Spin within a discrete-time theory
We prove that the classical theory with a discrete time (chronon) is a
particular case of a more general theory in which spinning particles are
associated with generalized Lagrangians containing time-derivatives of any
order (a theory that has been called "Non-Newtonian Mechanics"). As a
consequence, we get, for instance, a classical kinematical derivation of
Hamiltonian and spin vector for the mentioned chronon theory (e.g., in
Caldirola et al.'s formulation).Comment: 10 pages; LaTeX fil
Slower-than-Light Spin-1/2 Particles Endowed with Negative Mass Squared
Extending in a straightforward way the standard Dirac theory, we study a
quantum mechanical wave-equation describing free spinning particles --which we
propose to call "Pseudotachyons" (PT's)-- which behave like tachyons in the
momentum space, but like subluminal particles (v<c) in the ordinary space. This
is allowed since, as it happens in every quantum theory for spin-1/2 particles,
the momentum operator (that is conserved) and the velocity operator (that is
not) are independent operators, which refer to independent quantities. As a
consequence, at variance with ordinary Dirac particles, for PT's the average
velocity is not equal to the classical velocity, but actually to the velocity
"dual" of the classical velocity. The speed of PT's is therefore smaller than
the speed of light. Since a lot of experimental data seems to involve a
negative mass squared for neutrinos, we suggest that these particles might be
PT's, travelling, because of their very small mass, at subluminal speeds very
close to c. The present theory is shown to be separately invariant under the C,
P, T transformations; the covariance under Lorentz transformations is also
proved. Furthermore, we derive the kinematical constraints linking 4-impulse,
4-velocity and 4-polarization of free PT'sComment: LaTeX; 20 page
Energy Spread of the Unstable State and Proton Decay Observation
Because of the extreme smallness of the energy spread of the unstable state
describing the decaying proton, due in its turn to the anomalous smallness of
the resonance width expected for the proton decay, the application of the
Heisenberg time-energy relation predicts the measurement times for the proton
decay observation to be so long as to forbid a "continuous" observation of the
decay. This might account for the missing observation of the proton decay
Non-Newtonian Mechanics
The classical motion of spinning particles can be described without employing
Grassmann variables or Clifford algebras, but simply by generalizing the usual
spinless theory. We only assume the invariance with respect to the Poincare'
group; and only requiring the conservation of the linear and angular momenta we
derive the zitterbewegung: namely the decomposition of the 4-velocity in the
newtonian constant term p/m and in a non-newtonian time-oscillating spacelike
term. Consequently, free classical particles do not obey, in general, the
Principle of Inertia. Superluminal motions are also allowed, without violating
Special Relativity, provided that the energy-momentum moves along the worldline
of the center-of-mass. Moreover, a non-linear, non-constant relation holds
between the time durations measured in different reference frames. Newtonian
Mechanics is re-obtained as a particular case of the present theory: namely for
spinless systems with no zitterbewegung. Introducing a Lagrangian containing
also derivatives of the 4-velocity we get a new equation of the motion,
actually a generalization of the Newton Law a=F/m. Requiring the rotational
symmetry and the reparametrization invariance we derive the classical spin
vector and the conserved scalar Hamiltonian, respectively. We derive also the
classical Dirac spin and analyze the general solution of the Eulero-Lagrange
equation for Dirac particles. The interesting case of spinning systems with
zero intrinsic angular momentum is also studied.Comment: LaTeX; 27 page
Field theory of the spinning electron: Internal motions
We present here a field theory of the spinning electron, by writing down a
new equation for the 4-velocity field v^mu (different from that of Dirac
theory), which allows a classically intelligible description of the electron.
Moreover, we make explicit the noticeable kinematical properties of such
velocity field (which also result different from the ordinary ones). At last,
we analyze the internal zitterbewegung (zbw) motions, for both time-like and
light-like speeds. We adopt in this paper the ordinary tensorial language. Our
starting point is the Barut-Zanghi classical theory for the relativistic
electron, which related spin with zbw. This paper is dedicated to the memory of
Asim O. Barut, who so much contributed to clarifying very many fundamental
issues of physics, and whose work constitutes a starting point of these
articles.Comment: standard LaTeX fil
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