Running surface couplings

We discuss the renormalization group improved effective action and running surface couplings in curved spacetime with boundary. Using scalar self-interacting theory as an example, we study the influence of the boundary effects to effective equations of motion in spherical cap and the relevance of surface running couplings to quantum cosmology and symmetry breaking phenomenon. Running surface couplings in the asymptotically free SU(2) gauge theory are found.Comment: 11 pages, Latex fil

Alternating current losses in superconducting coils

Report examines relationship between coil loss and frequency and heat loss in coil as a function of the magnetic field H. Information is of value to manufacturers of superconducting magnets, motors and generators

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F(ϕ)RF(\phi)R coupling

Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $\xi \phi^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.Comment: 17 pages, 4 figure

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F(ϕ)RF(\phi)R coupling

Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $\xi \phi^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.Comment: 17 pages, 4 figure

Confinement and the quark Fermi-surface in SU(2N) QCD-like theories

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrated by means of a simple quark model.Comment: 5 pages, 2 figures, revised journal versio

Water-accelerated organic transformations

Rather than quenching all reactive intermediates and arresting the reaction, the addition of catalytic or stoichiometric (1-10 equiv.) quantities of H2O to organic and organometallic processes can lead to surprisingly beneficial effects on reaction rate, product yield, and regio-, diastereo- and enantioselectivity. A most intriguing aspect of H2O-promoted transformations is the role that this strong Lewis-base can play in providing a source for more highly Lewis-acidic species. This scenario is most likely operative when H2O is added to reaction mixtures containing alanes, but organozinc reagents or organocuprates also seem to be transformed accordingly. In addition, the oxide or hydroxide ligand on the metal presents a source for chelation interactions that change aggregation states of organometallics and can provide anchimeric assistance. In many cases, water has been found to be an effective hydrolyzing agent leading to secondary products that serve as catalysts or promoters. In some cases, it has been shown that water provides a quenching agent capable of driving chemical equilibria towards the desired products

Witten-Veneziano Relation for the Schwinger Model

The Witten-Veneziano relation between the topological susceptibility of puregauge theories without fermions and the main contribution of the completetheory and the corresponding formula of Seiler and Stamatescu with theso-called contact term are discussed for the Schwinger model on a circle. Usingthe (Euclidean) path integral and the canonical (Hamiltonian) approaches atfinite temperatures we demonstrate that both formulae give the same result inthe limit of infinite volume and (or) zero temperature

Relation between chiral symmetry breaking and confinement in YM-theories

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab initio continuum formulation of Yang-Mills theories, and the convergence of the mode sum is studied in detail. The mode sums are then explicitly calculated for the Schwinger model and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice gauge theory, the IR dominated mode sums are considered and the mode sum approximation to the static quark anti-quark potential is obtained numerically. We find a good agreement between the mode sum approximation and the static potential at large distances for the confinement and the high temperature plasma phase.Comment: 17 pages, 10 figures, typos corrected, references added, final version to appear in PR