We study the relativistic quark-antiquark system embedded in magnetic field (MF). The Hamiltonian containing confinement, one gluon exchange and spin-spin interaction is derived. We analytically follow the evolution of the lowest meson states as a functions of MF strength. Calculating the one gluon exchange interaction energy VOGE and spin-spin contribution aSS we have observed, that these corrections remain finite at large MF, preventing the vanishing of the total ρ meson mass at some Bcrit, as previously thought. We display the ρ masses as functions of MF in comparison with recent lattice data.

Perturbative gluon exchange interaction between quark and antiquark, or in a 3q system, is enhanced in a magnetic field and may cause vanishing of the total qq[over ¯] or 3q mass, and even unlimited decrease of it-recently called the magnetic collapse of QCD. The analysis of the one-loop correction below shows a considerable softening of this phenomenon due to qq[over ¯] loop contribution, similar to the Coulomb case of QED, leading to approximately logarithmic damping of gluon exchange interaction (≈O(1/ln|eB|)) at large magnetic field.

We investigate the electrical conductivity(EC) of dense quark matter in the vicinity of the phase transition line. We show that: (i) At high density Drude EC does not depend on the magnetic field up to eB ∼ 10 19 G. (ii) In the precritical region the fluctuation EC (paraconductivity) dominates over the Drude one. * borisk@itep.ru † andreichicov@mail.ru

Relativistic world-line Hamiltonian for strongly interacting 3q systems in magnetic field is derived from the path integral for the corresponding Green's function. The neutral baryon Hamiltonian in magnetic field obeys the pseudomomentum conservation and allows a factorization of the c.m. and internal motion. The resulting expression for the baryon mass in magnetic field is written explicitly with the account of hyperfine, OPE and OGE (color Coulomb) interaction. The neutron mass is fast decreasing with magnetic field, losing 1/2 of its value at eB ∼ 0.25 GeV 2 and is nearly zero at eB ∼ 0.5 GeV 2 . Possible physical consequences of the calculated mass trajectory of the neutron, M n (B), are presented and discussed.