Electrically neutral Dirac particles in the presence of external fields: exact solutions

In the present article we present exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments. Using the algebraic method of separation of variables, the Dirac equation is separated in cartesian, cylindrical and spherical coordinates, and exact solutions are obtained in terms of special functions.Comment: 20pp, IVIC-CFLE-93/02 (this is a version without Tex problems, the first version was corrupted

Radiative Effects in the Standard Model Extension

The possibility of radiative effects induced by the Lorentz and CPT non-invariant interaction term for fermions in the Standard Model Extension is investigated. In particular, electron-positron photo-production and photon emission by electrons and positrons are studied. The rates of these processes are calculated in the Furry picture. It is demonstrated that the rates obtained in the framework of the model adopted strongly depend on the polarization states of the particles involved. As a result, ultra-relativistic particles produced should occupy states with a preferred spin orientation, i.e., photons have the sign of polarization opposite to the sign of the effective potential, while charged particle are preferably in the state with the helicity coinciding with the sign of the effective potential. This leads to evident spatial asymmetries which may have certain consequences observable at high energy accelerators, and in astrophysical and cosmological studies.Comment: 10 pages, 2 figures, Revtex4, to appear in Phys.Rev.D, misprints are correcte

New bounds on neutrino magnetic moment and re-examination of plasma effect in neutrino spin light

Recent discussion on the possibility to obtain more stringent bounds on neutrino magnetic moment has stimulated new interest to possible effects induced by neutrino magnetic moment. In particular, in this note after a short review on neutrino magnetic moment we re-examine the effect of plasmon mass on neutrino spin light radiation in dense matter. We track the entry of the plasmon mass quantity in process characteristics and found out that the most substantial role it plays is the formation of the process threshold. It is shown that far from this point the plasmon mass can be omitted in all the corresponding physical quantities and one can rely on the results of massless photon spin light radiation theory in matter.Comment: to appear in Nuovo Cimento 35 C, No. 1, 2012 (based on the talk presented at the 25th Rencontres de Physique de la Vallee d'Aoste on "Results and Perspectives in Particle Physics", La Thuile, February 27 - March 5, 201

Neutrino spin oscillations in gravitational fields

We study neutrino spin oscillations in gravitational fields. The quasi-classical approach is used to describe the neutrino spin evolution. First we examine the case of a weak gravitational field. We obtain the effective Hamiltonian for the description of neutrino spin oscillations. We also receive the neutrino transition probability when a particle propagates in the gravitational field of a rotating massive object. Then we apply the general technique to the description of neutrino spin oscillations in the Schwarzschild metric. The neutrino spin evolution equation for the case of the neutrino motion in the vicinity of a black hole is obtained. The effective Hamiltonian and the transition probability are also derived. We examine the neutrino oscillations process on different circular orbits and analyze the frequencies of spin transitions. The validity of the quasi-classical approach is also considered.Comment: RevTeX4, 9 pages, 1 esp figure; article was revised, some misprints were corrected, 6 references added; accepted for publication in Int.J.Mod.Phys.

Bound-state beta-decay of a neutron in a strong magnetic field

The beta-decay of a neutron into a bound $(pe^-)$ state and an antineutrino in the presence of a strong uniform magnetic field ($B \gtrsim 10^{13}$ G) is considered. The beta-decay process is treated within the framework of the standard model of weak interactions. A Bethe-Salpeter formalism is employed for description of the bound $(pe^-)$ system in a strong magnetic field. For the field strengths $10^{13}$ G$\lesssim B \lesssim10^{18}$ G the estimate for the ratio of the bound-state decay rate $w_b$ and the usual (continuum-state) decay rate $w_c$ is derived. It is found that in such strong magnetic fields $w_b/w_c \sim 0.1-0.4$. This is in contrast to the field-free case, where $w_b/w_c \simeq 4.2 \times 10^{-6}$ [J. N. Bahcall, Phys. Rev. {\bf 124}, 495 (1961); L. L. Nemenov, Sov. J. Nucl. Phys. {\bf 15}, 582 (1972); X. Song, J. Phys. G: Nucl. Phys. {\bf 13}, 1023 (1987)]. The dependence of the ratio $w_b/w_c$ on the magnetic field strength $B$ exhibits a logarithmic-like behavior. The obtained results can be important for applications in astrophysics and cosmology.Comment: 22 pages (revtex4), 1 figure; v2: more detailed discussion on astrophysical applications in conclusion section, accepted for publication in Phys. Rev.

Quantum treatment of neutrino in background matter

Motivated by the need of elaboration of the quantum theory of the spin light of neutrino in matter ($SL\nu$), we have studied in more detail the exact solutions of the Dirac equation for neutrinos moving in the background matter. These exact neutrino wavefunctions form a basis for a rather powerful method of investigation of different neutrino processes in matter, which is similar to the Furry representation of quantum electrodynamics in external fields. Within this method we also derive the corresponding Dirac equation for an electron moving in matter and consider the electromagnetic radiation ("spin light of electron in matter", $SLe$) that can be emitted by the electron in this case.Comment: 10 pages, in: Proceedings of QFEXT'05 (The Seventh Workshop on Quantum Field Theory under the Influence of External Conditions, IEEC, CSIC and University of Barcelona, Barcelona, Catalonia, Spain, 5-9 September 2005.), ed. by Emilio Elizalde and Sergei Odintsov; published in Journal of Physics

Modification of Coulomb law and energy levels of the hydrogen atom in a superstrong magnetic field

We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: \Phi(z) = e/|z| [ 1- exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3 \pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 \pi B_{cr}/\alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.Comment: version to be published in Physical Review D (incorrect "Keywords" in previous version have been cancelled

The bremsstrahlung equation for the spin motion in LHC

The influence of the bremsstrahlung on the spin motion is expressed by the equation which is the analogue and generalization of the Bargmann-Michel-Telegdi equation. The new constant is involved in this equation. This constant can be immediately determined by the experimental measurement of the spin motion, or it follows from the classical limit of quantum electrodynamics with radiative corrections.Comment: 9 page

Chiral density waves in quark matter within the Nambu--Jona-Lasinio model in an external magnetic field

A possibility of formation of static dual scalar and pseudoscalar density wave condensates in dense quark matter is considered for the Nambu--Jona-Lasinio model in an external magnetic field. Within a mean-field approximation, the effective potential of the theory is obtained and its minima are numerically studied; a phase diagram of the system is constructed. It is shown that the presence of a magnetic field favors the formation of spatially inhomogeneous condensate configurations at low temperatures and arbitrary non-zero values of the chemical potential.Comment: 13 pages, 4 figure