Search Results (3)

An extension of the Dirac equation for an initially massless particle carrying an electric charge, assumed to be embedded via minimal coupling into an external fluctuating electromagnetic four-potential of the vacuum, is suggested. We conjecture that appropriate averages of the four-vector can lead to observable quantities, such as a particle mass in its rest frame. The conditions on the potential mean values to become gauge-invariant are obtained. The mass is found to be proportional to the magnitude of the charge times the associated mean Lorentz scalar of the four-potential, and the relation holds for both spacelike and timelike types of four-vectors. For the latter, the extended Dirac equation violates Lorentz covariance, but the violation can be argued to occur within a time scale allowed by the uncertainty principle. For larger times, the particle has acquired a mass and Lorentz covariance is restored. This mathematical scenario is applied to acquire estimates of the neutrino millicharge and magnetic moment, in good agreement with the present upper bounds obtained experimentally. The issue of unstable particle decay is considered by focusing, for illustration, on the main decay channels of the selected particles. From the lifetime of the $\tau$ lepton, a lower bound of the effective neutrino mass is predicted, which can be tested in future experiments. Full article

We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes its sign adiabatically. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with a proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as a function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born–Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime. Full article

We consider a quantum spinless nonrelativistic charged particle moving in the $xy$ plane under the action of a time-dependent magnetic field, described by means of the linear vector potential $\mathbf{A}=B(t)\left[-y(1+\alpha ),x(1-\alpha )\right]/2$, with two fixed values of the gauge parameter $\alpha$: $\alpha =0$ (the circular gauge) and $\alpha =1$ (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for $\alpha =0$ and straight lines for $\alpha =1$. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function $B(t)$. They are expressed in terms of solutions to the classical equation of motion $\ddot{\epsilon }+{\omega }_{\alpha }^2(t)\epsilon =0$, with ${\omega }_1=2{\omega }_0$. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions $B(t)$, when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value. Full article