Giovanni Salesi

Spin and electron structure

The recent literature shows a renewed interest, with various independent approaches, in the classical theories 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 theories, 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 linearization)— it transforms into the ordinary Dirac equation (valid for the electron as a whole). PACS nos.: 03.70.+k ; 11.10.Qr ; 14.60.Cd . 0 † Work partially supported by INFN, CNR, MURST; by CAPES, CNPq, FAPESP; and by the Slovenian Ministry of Science and Technology. 0∗ On leave from the J.Stefan Institute; University of Ljubljana; 61111–Ljubljana; Slovenia. 0∗∗ Also: Facolta di Ingegneria, Universita statale di Bergamo, 24044 Dalmine (BG), Italy; and C.C.S., State University at Campinas, 13083-970 Campinas, S.P.; Brazil. 0∗∗∗ On leave from Departamento de Matematica Aplicada — Imecc; UNICAMP; 13084–Campinas, S.P.; Brazil.Abstract 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 linearization) — it transforms into the ordinary Dirac equation (valid, of course, for the electron as a whole).

About Zitterbewegung and Electron Structure

Abstract We start from the spinning electron model by Barut and Zanghi, which has been recently translated into the Clifford algebra language. We “complete” such a translation, first of all, by expressing in the Clifford formalism a particular Barut-Zanghi (BZ) solution, which refers (at the classical limit) to an “internal” helical motion with a time-like speed (and is here shown to originate from the superposition of positive and negative frequency solutions of the Dirac equation). Then, we show how to construct solutions of the Dirac equation describing helical motions with light-like speed, which meet very well the standard interpretation of the velocity operator in the Dirac equation theory (and agree with the solution proposed by Hestenes, on the basis — however — of ad-hoc assumptions that are unnecessary in the present approach). The above results appear to support the conjecture that the zitterbewegung motion (a helical motion, at the classical limit) is responsible for the electron spin.

A Velocity Field and Operator for Spinning Particles in (Nonrelativistic) 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 language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin-

Complex-barrier tunnelling times

{\frac{1}{2}}

Field theory of the spinning electron and internal motions

particle. This operator appears as 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 (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. 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 the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector.

High sensitivity measurements of thermal properties of textile fabrics

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 Hartman-Fletcher effect, and find that it is suppressed by the presence of a (non negligible) imaginary potential. In fact, when a suffficiently 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 expectation.

Hydrodynamical Reformulation and Quantum Limit of The Barut–Zanghi Theory

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.

Laboratory bounds on Lorentz symmetry violation in low energy neutrino physics

A new testing apparatus is proposed to measure the thermal properties of fabrics made from polymeric materials. The calibration of the apparatus and the data acquisition procedure are considered in detail in order to measure thermal conductivity, resistance, absorption and diffusivity constants of the tested fabric samples. Differences between dry and wet fabrics have been carefully detected and analyzed. We have developed a new measurement protocol, the ThermoTex protocol, which agrees with the UNI EN 31092 standard and entails accurate quantification of the experimental errors according to a standard statistical analysis, thus allowing a rigorous investigation of the physical behavior of the phenomena involved. As a consequence, our equipment exhibits great potential for optimizing the thermal comfort of fabrics, according to the market demand, thanks to the possible development of a predictive phenomenological theory of the effects involved.

Describing Sr2RuO4 superconductivity in a generalized Ginzburg–Landau 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 for a hydrodynamical reformulation of the BZ theory. Working out a “probabilistic fluid,” we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to “quantize” the BZ theory: by employing this time the tensorial language, more popular in first-quantization. “Quantizing” the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual “quantum limit” of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical “Weyssenhoff fluid,” while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.

NONRELATIVISTIC CLASSICAL MECHANICS FOR SPINNING PARTICLES

Quantitative bounds on Lorentz symmetry violation in the neutrino sector have been obtained by analyzing existing laboratory data on neutron β decay and pion leptonic decays. In particular some parameters appearing in the energy–momentum dispersion relations for νe and νμ have been constrained in two typical cases arising in many models accounting for Lorentz violation.