The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.Comment: Latex2e, 14 pages, 5 figure

The mass function of GX 339-4 from spectroscopic observations of its donor star

We obtained 16 VLT/X-shooter observations of GX 339-4 in quiescence in the period May - September 2016 and detected absorption lines from the donor star in its NIR spectrum. This allows us to measure the radial velocity curve and projected rotational velocity of the donor for the first time. We confirm the 1.76 day orbital period and we find that $K_2$ = $219 \pm 3$ km s$^{-1}$, $\gamma = 26 \pm 2$ km s$^{-1}$ and $v \sin i = 64 \pm 8$ km s$^{-1}$. From these values we compute a mass function $f(M) =1.91 \pm 0.08~M_{\odot}$, a factor $\sim 3$ lower than previously reported, and a mass ratio $q = 0.18 \pm 0.05$. We confirm the donor is a K-type star and estimate that it contributes $\sim 45-50\%$ of the light in the $J$- and H-band. We constrain the binary inclination to $37^\circ < i < 78^\circ$ and the black hole mass to $2.3~M_{\odot} < M_\mathrm{BH} < 9.5~M_{\odot}$. GX 339-4 may therefore be the first black hole to fall in the 'mass-gap' of $2-5~M_{\odot}$.Comment: 11 pages, 7 figures, accepted for publication in Ap

Discovery of X-ray Jets in the Microquasar H 1743-322

We report on the formation and evolution of two large-scale, synchrotron-emitting jets from the black hole candidate H 1743-322 following its reactivation in 2003. In November 2003 after the end of its 2003 outburst, we noticed, in observations with the Australia Telescope Compact Array, the presence of a new and variable radio source about 4.6" to the East of H 1743-322, that was later found to move away from H 1743-322. In February 2004, we detected a radio source to the West of H 1743-322, symmetrically placed relative to the Eastern jet. In 2004, follow-up X-ray observations with {\em Chandra} led to the discovery of X-ray emission associated with the two radio sources. This likely indicates that we are witnessing the interaction of relativistic jets from H 1743-322 with the interstellar medium causing in-situ particle acceleration. The spectral energy distribution of the jets during the decay phase is consistent with a classical synchrotron spectrum of a single electron distribution from radio up to X-rays, implying the production of very high energy ($>$ 10 TeV) particles in those jets. We discuss the jet kinematics, highlighting the presence of a significantly relativistic flow in H 1743-322 almost a year after the ejection event.Comment: Accepted for publication in The Astrophysical Journal. 17 pages, 9 figure

Dirac equation for membranes

Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of positive and negative masses (tension). There are no tachyonic solutions.Comment: 5 pages, 1 figure, v2: improved version, accepted for publication as a Brief Report in Physical Review

Stirling cycle cryogenic cooler

A long lifetime Stirling cycle cryogenic cooler particularly adapted for space applications is described. It consists of a compressor section centrally aligned end to end with an expansion section, and respectively includes a reciprocating compressor piston and displacer radially suspended in interconnecting cylindrical housings by active magnetic bearings and has adjacent reduced clearance regions so as to be in noncontacting relationship therewith and wherein one or more of these regions operate as clearance seals. The piston and displacer are reciprocated in their housings by linear drive motors to vary the volume of respectively adjacent compression and expansion spaces which contain a gaseous working fluid and a thermal regenerator to effect Stirling cycle cryogenic cooling

Electromagnetism and multiple-valued loop-dependent wave functionals

We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.Comment: 5 page