Multipolar Expansions for the Relativistic N-Body Problem in the Rest-Frame Instant Form

Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyperplanes (intrinsic rest frame of the isolated system) turn out to be the natural framework for describing multipole kinematics. In particular, concepts like the {\it barycentric tensor of inertia} can be defined in special relativity only by means of the quadrupole moments of the isolated system.Comment: 46 pages, revtex fil

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

Hermitian vector fields and special phase functions

We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a fibred manifold over absolute time equipped with a spacelike Riemannian metric, a spacetime connection (preserving the time fibring and the spacelike metric) and an electromagnetic field. In the second case, we consider a spacetime equipped with a Lorentzian metric and an electromagnetic field. In both cases, we exhibit a natural Lie algebra of special phase functions and show that the Lie algebra of Hermitian vector fields turns out to be naturally isomorphic to the Lie algebra of special phase functions. Eventually, we compare the Galilei and Einstein cases

C^{2} formulation of Euler fluid

The Hamiltonian formalism for the continuous media is constructed using the representation of Euler variables in $\mathcal{C}^{2}\times \infty$ phase space.Comment: 8 page

Elementary particle interaction from a Kaluza-Klein scheme

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure. Finally applications to the Electro-Weak model are presented.Comment: 8 pages, Proceedings of the II Stueckelberg worksho

Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Massive relativistic particle model with spin from free two-twistor dynamics and its quantization

We consider a relativistic particle model in an enlarged relativistic phase space M^{18} = (X_\mu, P_\mu, \eta_\alpha, \oeta_\dalpha, \sigma_\alpha, \osigma_\dalpha, e, \phi), which is derived from the free two-twistor dynamics. The spin sector variables (\eta_\alpha, \oeta_\dalpha, \sigma_\alpha,\ osigma_\dalpha) satisfy two second class constraints and account for the relativistic spin structure, and the pair (e,\phi) describes the electric charge sector. After introducing the Liouville one-form on M^{18}, derived by a non-linear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wavefunction provides a generating functional for free, massive higher spin fields.Comment: FTUV-05-0919, IFIC-05-46, IFT UWr 0110/05. Plain latex file, no macros, 22 pages. A comment and references added. To appear in PRD1

On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

SOT-MRAM 300mm integration for low power and ultrafast embedded memories

We demonstrate for the first time full-scale integration of top-pinned perpendicular MTJ on 300 mm wafer using CMOS-compatible processes for spin-orbit torque (SOT)-MRAM architectures. We show that 62 nm devices with a W-based SOT underlayer have very large endurance (> 5x10^10), sub-ns switching time of 210 ps, and operate with power as low as 300 pJ.Comment: presented at VLSI2018 session C8-