Neutral relativistic two-body problem in a constant magnetic field

H. Pierre Noyes, Edwin D. Jones

Philippe Droz-Vincent

The pseudomomentum is conserved for a single charge in any constant (over space and time) electromagnetic field. It is also conserved for a neutral two-body system, not only in a pure (constant) magnetic field, but also in a pure (constant) electric field, and explicit wave equations can be written. A neutral two-body system in a constant electric field is treated in a way that parallels our previous approach to this system in a constant magnetic field. Relative motion is separated, but the relative time now survives, whereas a spacelike degree of freedom gets eliminated. In other cases, there is, in general, no evidence of a closed form of the wave equations, but conservation of the pseudomomentum can be required as a reasonable condition for implicitly determining the so-called ``three-body terms'' in the wave equation.

V. S. Bhasin, H. Jacob, Asoke N. Mitra

LC. Suárez-González, Gretel Quintero Angulo, A. Pérez Martínez +1 more

Abstract We study the thermodynamic properties of a neutral vector boson gas in presence of a constant magnetic field, by means of a semi-classical approach that allows to introduce the spin in the non-relativistic spectrum of the bosons. Bose-Einstein condensation is obtained and it turns out to depend on all the parameters involved in the problem: temperature, particle density and magnetic field. A spontaneous magnetization appears at low temperature as a consequence of the condensed state. The axial symmetry imposed in the system by the magnetic field presence, splits the pressure in two components, one along and another perpendicular to the magnetic axis. Under certain conditions, the perpendicular pressure becomes negative signaling that the system undergoes a transversal magnetic collapse. The spontaneous magnetization might be useful to model magnetic field production inside compact stars, while the negative pressures imposes certain limits to the temperatures and densities needed inside these objects to support a given magnetic field.

Tihomir G. Tenev, Nikolay V. Vitanov

Zitterbewegung of neutral relativistic particles propagating along a constant magnetic and/or electric field is studied. It is shown that spin Zitterbewegung, when superimposed on the Larmor precession frequency, leads to a beating pattern. The existence of a forbidden frequency of spin precession is predicted. Modifications of position and velocity Zitterbewegung due to lifted spin degeneracy manifested in the appearance of longitudinal and transversal Zitterbewegung, each with two Zitterbewegung frequencies and resulting beating patterns, are reported.

V. M. Vinogradov