arXiv subjects

Giovanni Salesi

Publications and source records attributed to Giovanni Salesi.

17 recordsLinked to original sources

arXiv2017

Field Theory of the Electron, Spin and Zitterbewegung

In previous papers, we have investigated the classical theory of Barut and Zanghi (BZ) for the electron spin [which interpreted the Zitterbewegung (zbw) motion as an internal motion along helical paths], and its "quantum" version, by using the language of Clifford algebras. And, in so doing, we ended with a new non-linear Dirac-like equation (NDE). We want to readdress in this Review the whole subject, and extend it, by translating it however into the ordinary tensorial language, within the frame of the first quantization formalism. In particular, we re-derive here the NDE for the electron field, and show it to be associated with a new conserved probability current (which allows us to work out a quantum probabilistic interpretation of our NDE). Actually, the Dirac equation is obtained from the former NDE just by averaging over a zbw cycle. We then derive an equation of motion for the 4-velocity field which will allow us to regard the electron as an extended-type object with a classically intelligible internal structure. We carefully study the solutions of the NDE; with special attention to those implying (at the classical limit) light-like helical motions, which appear to be the most adequate solutions for the electron description from a kinematical and physical point of view, and do cope with the electromagnetic properties of the electron. At last we propose a natural generalization of our approach, for the case in which an external electromagnetic potential A^μis present; it happens to be based on a new system of five first-order differential field equations.

hep-th↗

arXiv2015

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.

hep-th↗

arXiv2011

Lorentz-violating dynamics in the pre-Planckian Universe

We have recently proposed a Lorentz-violating energy-momentum relation entailing an exact momentum cutoff and studied various physical applications of that dispersion law. By a simple phenomenological approach we here study Lorentz violation effects on early Universe and pre-Planckian cosmological radiation. In particular, we predict an effective infinite speed of light soon after the Big Bang instant, leading to a straightforward solution of the horizon and flatness problems without recourse to inflation, cosmological scalar fields or other ad hoc energy sources.

gr-qc↗

arXiv2009

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.

quant-ph↗

arXiv2007

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).

quant-ph↗

arXiv2006

Deriving Spin of the Bosonic String

Exploiting the strict analogy between the motion of strings and extended-like spinning particles, we propose an original kinematical formulation of the spin of bosonic strings and give, for the first time, an analytical derivation of an explicit expression of the string spin vector.

hep-th↗

arXiv2002

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.

quant-ph↗

arXiv2002

Spin and Electron Structure

The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore their physical and mathematical meaning, by the natural and powerful language of Clifford algebras (which, incidentally, will allow us to unify those different approaches). In such models, the ordinary electron is in general associated to the mean motion of a point--like "constituent" Q, whose trajectory is a cylindrical helix. We find, in particular, that the object Q obeys a new, non-linear Dirac--like equation, such that --when averaging over an internal cycle (which corresponds to a linearization)-- it transforms into the ordinary Dirac equation (valid, of course, for the electron as a whole).

quant-ph↗

arXiv2002

Complex--Barrier Tunnelling Times

In this paper we calculate the analytic expression of the phase time for the scattering of an electron off a complex square barrier. As is well known the (negative) imaginary part of the potential takes into account, phenomenologically, the absorption. We investigate the so-called Hartman-Fletcher effect, and find that it is suppressed by the presence of a (not negligible) imaginary potential. In fact, when a sufficiently large absorption is present, the asymptotical transmission speed is finite. Actually, the tunnelling time does increase linearly with the barrier width. A recent optical experiment seems to be in agreement with our theoretical previsions.

quant-ph↗

arXiv2002

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's

quant-ph↗

arXiv2002

Superluminal effects for quantum tunneling through two successive barriers

We study the phenomenon of one-dimensional non-resonant tunnelling through two successive potential barriers, separated by an intermediate free region R, by analyzing the relevant solutions to the Schroedinger equation. We find that the total traversal time is INDEPENDENT not only of the barrier widths (the so-called "Hartman effect"), but also of the R-width: so that the effective velocity in the region R, between the two barriers, can be regarded as infinite. This agrees with the results known from the corresponding waveguide experiments, which simulated the tunnelling experiment herein considered because of the formal identity between the Schroedinger and the Helmholtz equation [PACS numbers: 73.40.Gk; 03.65.-w; 03.30.+p; 41.20.Jb; 84.40.Az].

quant-ph↗

arXiv1998

Spin effects on the cyclotron frequency for a Dirac electron

The Barut--Zanghi (BZ) theory can be regarded as the most satisfactory picture of a classical spinning electron and constitutes a natural "classical limit" of the Dirac equation. The BZ model has been analytically studied in some previous papers of ours in the case of free particles. By contrast, in this letter we consider the case of external fields, and a previously found equation of the motion is generalized for a non-free spin-1/2 particle. In the important case of a spinning charge in a uniform magnetic field, we find that its angular velocity (along its circular orbit around the magnetic field direction) is slightly different from the classical "cyclotron frequency" eH/m which is expected to hold for spinless charges. As a matter of fact, the angular velocity results to depend on the spin orientation. As a consequence, the electrons with magnetic moment mu parallel to the magnetic field do rotate with a frequency greater than that of electrons endowed with mu antiparallel to H.

hep-th↗

arXiv1996

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.

quant-ph↗

arXiv1996

The spinning electron: Hidrodynamical formulation, and quantum limit, of the Barut-Zanghi theory

One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited and fruitful for a hydrodynamical re-formulation of the BZ theory. Working out, in such a way, a ``probabilistic fluid'', we are allowed to re-interpret the original classical spinors as quantum wave-functions for the electron. Thus, we can pass to ``quantize" the BZ theory employing this time the tensorial language, more popular in first-quantization. ``Quantizing'' the BZ theory, however, does not lead to the Dirac equation, but rather to a non-linear, Dirac--like equation, which can be regarded as the actual ``quantum limit'' of the BZ classical theory. Moreover, an original variational approach to the the BZ probabilistic fluid shows that it is a typical ``Weyssenhoff fluid'', while the Hamilton-Jacobi equation (linking together mass, spin and zbw frequency) appears to be nothing but a special case of de Broglie's famous energy-frequency relation. Finally, after having discussed the remarkable correlation between the gauge transformation U(1) and a general rotation on the spin plan, we clarify and comment on the two-valuedness nature of the fermionic wave-function, and on the parity and charge conjugation transformations.

hep-th↗

arXiv1996

About the kinematics of spinning particles

Inserting the correct Lorentz factor into the definition of the 4-velocity v^mu for spinning particles entails new kinematical properties for v^2. The well-known constraint (identically true for scalar particles, but entering also the Dirac theory, and assumed a priori in all spinning particle models) p_mu v^mu = m is here derived in a self-consistent way.

hep-th↗

arXiv1996

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.

hep-th↗

arXiv1996

Velocity field and operator in (non relativistic) quantum mechanics

Starting from the formal expressions of the hydrodynamical (or ``local'') quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce --in terms of the ordinary tensorial framework-- a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called zitterbewegung, which is the spin ``internal'' motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelung fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector.

hep-th↗