We study the correlator of two vector currents in quenched SU (2) lattice gauge theory with a chirally invariant lattice Dirac operator with a constant external magnetic field. It is found that in the confinement phase the correlator of the components of the current parallel to the magnetic field decays much slower than in the absence of a magnetic field, while for other components the correlation length slightly decreases. We apply the maximal entropy method to extract the corresponding spectral function. In the limit of zero frequency this spectral function yields the electric conductivity of the quenched theory. We find that in the confinement phase the external magnetic field induces nonzero electric conductivity along the direction of the field, transforming the system from an insulator into an anisotropic conductor. In the deconfinement phase the conductivity does not exhibit any sizable dependence on the magnetic field.Recently, heavy ion experiments at the BNL Relativistic Heavy Ion Collider (RHIC) have found an evidence [1] for the so-called chiral magnetic effect [2] in quarkgluon plasma. The essence of the effect is the generation of electric current along the direction of the external magnetic field in the background of topologically nontrivial gauge field configurations. Experimentally, the effect manifests itself as the dynamical enhancement of fluctuations in the numbers of charged hadrons emitted above and below the reaction plane in off-central heavyion collisions. Recently this effect has been studied also in lattice gauge theory, and the evidence for charge separation in magnetic field has been found [3,5]. In [3] it has been found that the fluctuations of the electric current along the magnetic field are strongly enhanced as compared to the fluctuations of current in the perpendicular directions. This conclusion was also confirmed by an analytical calculation in the instanton gas model [6]. The result of [3] on the difference of longitudinal and transverse electric current susceptibilities has been reproduced later by an analytical calculation [7]; the frequency dependence of the conductivity has also been evaluatedfor the weak coupling result, see [8].A natural question to ask is whether this enhancement of current fluctuations corresponds to a real flow of charge, or is just caused by short-lived quantum fluctuations. This question can be answered by studying the current-current correlation functions. The currents which correspond to a real transport of charged particles should have long-range correlations in time, while quantum fluctuations are typically characterized by a fi-nite correlation time [9]. Recalling Green-Kubo relations, one can see that this property is intimately related to the electric conductivity -namely, the real transport of charged particles can occur only in conducting media.

We explore the masses (ground states energies) of neutral and charged ρ mesons in strong abelian magnetic field in SU(3) gluodynamics. The energies of these particle in the external magnetic field depends on its spin projection s z on the axis of external magnetic field. The masses of ρ 0 meson with s z = ±1 increase with the field. The masses of ρ ± mesons with zero spin also grow with the magnetic field. The ground state energies of ρ − meson with s z = −1 and ρ + meson with s z = +1 decrease as a function of the field, while the energies of ρ + meson with s z = −1 and ρ − meson with s z = +1 rise with the field value.

We computed correlators of vector, axial and pseudoscalar currents in the external strong magnetic field according to SU(2) lattice gauge theory. Masses of the neutral ρ and A mesons with different spin projections s = 0, ±1 along the magnetic field direction have been calculated. The masses of the neutral axial and vector mesons with zero spin s = 0 decrease under the increasing magnetic field, while the masses with spin s = ±1 increase with the value of the field. The quark mass extrapolation also were performed on the lattice.

We explore the masses (ground states energies) of neutral and charged ρ mesons in strong abelian magnetic field in SU(3) gluodynamics. The energies of these particle in the external magnetic field depends on its spin projection s z on the axis of external magnetic field. The masses of ρ 0 meson with s z = ±1 increase with the field. The masses of ρ ± mesons with zero spin also grow with the magnetic field. The ground state energies of ρ − meson with s z = −1 and ρ + meson with s z = +1 decrease as a function of the field, while the energies of ρ + meson with s z = −1 and ρ − meson with s z = +1 rise with the field value.

A possible experimental observation of the chiral magnetic effect in heavy ion collisions at RHIC was recently reported by the STAR Collaboration. We study signatures of this effect in SU(2) lattice gluodynamics with the chirally invariant Dirac operator. We find that at zero temperature the local fluctuations of an electric current of quarks and chirality fluctuations increase with a growth of an abelian external magnetic field. The external magnetic field leads to a spatial separation of the quark's electric charges. The separation increases with the strength of the magnetic field. As temperature gets higher the dependence of these quantities on the strength of the magnetic field becomes weaker. In the deconfinement phase the local fluctuations of the chiral density and of the spatial components of the quarks electric current are large and are almost independent on the external magnetic field. The local fluctuations of the electric charge density decrease with the strength of the magnetic field in this phase.