Beyond-Constant-Mass-Approximation Magnetic Catalysis in the Gauge Higgs-Yukawa Model

Beyond-constant-mass approximation solutions for magnetically catalyzed fermion and scalar masses are found in a gauge Higgs-Yukawa theory in the presence of a constant magnetic field. The obtained fermion masses are several orders of magnitude larger than those found in the absence of Yukawa interactions. The masses obtained within the beyond-constant-mass approximation exactly reduce to the results within the constant-mass approach when the condition $\nu \ln (\frac{1}{\hat{m}^{2}})\ll 1$ is satisfied. Possible applications to early universe physics and condensed matter are discussed.Comment: Revised numerical results. New figures. Several sections rewritte

Long range neutrino forces in the cosmic relic neutrino background

Neutrinos mediate long range forces among macroscopic bodies in vacuum. When the bodies are placed in the neutrino cosmic background, these forces are modified. Indeed, at distances long compared to the scale $T^{-1}$, the relic neutrinos completely screen off the 2-neutrino exchange force, whereas for small distances the interaction remains unaffected.Comment: 8 pages, 2 figure

Perturbation expansion for 2-D Hubbard model

We develop an efficient method to calculate the third-order corrections to the self-energy of the hole-doped two-dimensional Hubbard model in space-time representation. Using the Dyson equation we evaluate the renormalized spectral function in various parts of the Brillouin zone and find significant modifications with respect to the second-order theory even for rather small values of the coupling constant U. The spectral function becomes unphysical for $U \simeq W$, where W is the half-width of the conduction band. Close to the Fermi surface and for U<W, the single-particle spectral weight is reduced in a finite energy interval around the Fermi energy. The increase of U opens a gap between the occupied and unoccupied parts of the spectral function.Comment: 17 pages, 11 Postscript figures, Phys. Rev. B, accepte

Mesons and diquarks in neutral color superconducting quark matter with β\beta-equilibrium

The spectrum of meson and diquark excitations in cold color-superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with $\beta$-equilibrium. A 2-flavored Nambu--Jona-Lasinio type model including a baryon $\mu_B$, color $\mu_8$, and electric $\mu_Q$ chemical potentials is used. Two relations between coupling constants $H$ and $G$ in the diquark- and quark-antiquark channels, correspondingly, are treated, $H=3G/4$ and $H=G$. At $H=3G/4$ the gapless- and at $H=G$ the gapped neutral color superconductivity is realized. It is shown that color and electrical neutrality together with $\beta$-equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non--neutral matter. It is also shown that the properties of the physical $SU(2)_c$-singlet diquark excitation in the 2SC ground state varies for different parameterization schemes. Thus, for $H=3G/4$ one finds a heavy resonance with mass $\sim$ 1100 MeV in the non--neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass $\sim\mu_Q\sim$ 200 MeV appears in the gapless 2SC phase. For $H=G$, there is again a resonance (with the mass $\sim$ 300 MeV) in the neutral gapped 2SC phase. Hence, the existence of the stable massive SU(2)$_c$-singlet diquark excitation is a new peculiarity of the gapless 2SC.Comment: 18 pages, 9 figures; version accepted for publication in PR

s-s*-d-wave superconductor on a square lattice and its BCs phase diagram

We study an extended Hubbard model with on-site repulsion and nearest neighbors attraction which tries to mimic some of the experimental features of doped cuprates in the superconducting state. We draw and discuss the phase diagram as a function of the effective interactions among electrons for a wide range of doping concentrations. We locate the region which is relevant for the cuprates setting some constraints on the parameters which may be used in this kind of effective models. We also study the effects of temperature and orthorrombicity on the symmetry and magnitude of the gap function, and map the model onto a simpler linearized hamiltonian, which produces similar phase diagrams.Comment: 4 pages, 3 figures included. Accepted for publication in Phys. Rev.

Modified Spin Wave Thoery of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest and next-nearest neighbour intralayer interaction is studied by means of the modified spin wave method. For weak interlayer coupling, the ground state is found to be always magnetically ordered while the quantum disordered phase appear for large enough interlayer coupling. The properties of the disordered phase vary according to the strength of the frustration. In the regime of weak frustration, the disordered ground state is an almost uncorrelated assembly of interlayer dimers, while in the strongly frustrated regime the quantum spin liquid phase which has considerable N\'eel type short range order appears. The behavior of the sublattice magnetization and spin-spin correlation length in each phase is discussed.Comment: 15 pages, revtex, figures upon reques

Large N dynamics in QED in a magnetic field

The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of 1/N expansion. The existence of a threshold value N_{thr}, dividing the theories with essentially different dynamics, is established. For the number of flavors N << N_{thr}, the dynamical mass is very sensitive to the value of the coupling constant \alpha_b, related to the magnetic scale \mu = |eB|. For N of order N_{thr} or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with cutoff of order |eB| and the dimensional coupling constant G \sim 1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially \alpha_b independent (the dynamics with an infrared stable fixed point). The value of N_{thr} separates a weak coupling dynamics (with \tilde{\alpha}_b \equiv N\alpha_b << 1) from a strong coupling one (with \tilde{\alpha}_b \gtrsim 1) and is of order 1/\alpha_b.Comment: 4 pages, REVTe

Ward-Takahashi Identity with External Field in Ladder QED

We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED.Comment: new references(refs.10,11) added, 18 pages, Late

Families of Canonical Transformations by Hamilton-Jacobi-Poincar\'e equation. Application to Rotational and Orbital Motion

The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.Comment: 21 page