A novel strong coupling expansion of the QCD Hamiltonian

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in \lambda = g^{-2/3} can be obtained. The free part is the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and the interaction terms proportional to \lambda^n contain n discretised spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order \lambda^2 for the case of SU(2) Yang-Mills theory.Comment: Talk given at the 6th International Workshop on "Critical Point and Onset of Deconfinement (CPOD)", Dubna, Russia, 23-29 August 201

On Unconstrained SU(2) Gluodynamics with Theta Angle

The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing theta angle. It is shown that for any theta angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained nonlocal theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different theta angles are canonically equivalent as on the original constrained level.Comment: 13 pages Revtex, no figures; several misprints corrected; version to appear in Eur. Phys. J.

Sufficient conditions for the anti-Zeno effect

The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge

Theory of non-Fermi liquid and pairing in electron-doped cuprates

We apply the spin-fermion model to study the normal state and pairing instability in electron-doped cuprates near the antiferromagnetic QCP. Peculiar frequency dependencies of the normal state properties are shown to emerge from the self-consistent equations on the fermionic and bosonic self-energies, and are in agreement with experimentally observed ones. We argue that the pairing instability is in the $d_{x^{2}-y^{2}}$ channel, as in hole-doped cuprates, but theoretical $T_{c}$ is much lower than in the hole-doped case. For the same hopping integrals and the interaction strength as in hole-doped materials, we obtain $T_{c}\sim10$K at the end point of the antiferromagnetic phase. We argue that a strong reduction of $T_{c}$ in electron-doped cuprates compared to hole-doped ones is due to critical role of the Fermi surface curvature for electron-doped materials. The $d_{x^{2}-y^{2}}$-pairing gap $\Delta(\mathbf{k},\omega)$ is strongly non-monotonic along the Fermi surface. The position of the gap maxima, however, does not coincide with the hot spots, as the non-monotonic $d_{x^{2}-y^{2}}$ gap persists even at doping when the hot spots merge on the Brillouin zone diagonals.Comment: 16 page

Gravitational and electromagnetic fields near an anti-de Sitter-like infinity

We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.Comment: 4 pages, 2 figure