Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie

An Investigation of the Soft Pion Relation in Quenched Lattice QCD

A lattice determination of the form factor and decay constants for the semileptonic decay of heavy pseudoscalar (PS) mesons at zero recoil is presented from which the soft pion relation is satisfied. Chiral extrapolation of the form factor is performed at constant $q^2$. Pole dominance is used to extrapolate the form factor in heavy quark mass. At the B mass, the form factor at zero recoil lies somewhat below the ratio of decay constants; the relation remains satisfied within error.Comment: 3 pages, 2 figure

Brane Induced Gravity, its Ghost and the Cosmological Constant Problem

"Brane Induced Gravity" is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed analysis of codimension > 2 models employing gauge invariant variables in a flat background approximation. It is argued that using instead a curved background sourced by the brane would not resolve the ghost issue, unless a very specific condition is satisfied (if satisfiable at all). As for other properties of the model, from an explicit analysis of the 4-dimensional graviton propagator we extract a mass, a decay width and a momentum dependent modification of the gravitational coupling for the spin 2 mode. In the flat space approximation, the mass of the problematic spin 0 ghost is instrumental in filtering out a brane cosmological constant. The mass replaces a background curvature that would have had the same function. The optical theorem is used to demonstrate the suppression of graviton leakage into the uncompactified bulk. Then, we derive the 4-dimensional effective action for gravity and show that general covariance is spontaneously broken by the bulk-brane setup. This provides a natural realization of the gravitational Higgs mechanism. We also show that the addition of extrinsic curvature dependent terms has no bearing on linearized brane gravity.Comment: v2: LaTeX, JHEP style, 41 pages, 3 eps figures. Partly rewritten to improve presentation, results unchanged, published versio

On an asymptotic estimate of the nn-loop correction in perturbative QCD

A recently proposed method of estimating the asymptotic behaviour of QCD perturbation theory coefficients is critically reviewed and shown to contain numerous invalid mathematical operations and unsubstantiated assumptions. We discuss in detail why this procedure, based solely on renormalization group (RG) considerations and analyticity constraints, cannot lead to such estimates. We stress the importance of correct renormalization scheme (RS) dependence of any meaningful asymptotic estimate and argue that the unambiguous summation of QCD perturbation expansions for physical quantities requires information from outside of perturbation theory itself.Comment: PRA-HEP-92/17, Latex, 20 pages of text plus 5 figures contained in 5 separate PS files. Four of them (corresponding to Figs.1,2,3,5) are appended at the end of this file, the (somewhat larger one) corresponding to Fig.4 can be obtained from any of the mentioned E-mail addresses upon request. E-mail connections: J. Chyla - [email protected]) or h1kchy@dhhdesy3 P. Kolar - [email protected]

Energy States of Colored Particle in a Chromomagnetic Field

The unitary transformation, which diagonalizes squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of diagonalized Hamiltonian, that describe the states with definite value of energy and call them energy states. It is pointed out that, the energy states are determined by the color interaction term of the particle with the background chromofield and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian, that ensure the superpartner property of the energy states.Comment: 25 pages, some calculation details have been removed, typos correcte

Light propagation in non-trivial QED vacua

Within the framework of effective action QED, we derive the light cone condition for homogeneous non-trivial QED vacua in the geometric optics approximation. Our result generalizes the ``unified formula'' suggested by Latorre, Pascual and Tarrach and allows for the calculation of velocity shifts and refractive indices for soft photons travelling through these vacua. Furthermore, we clarify the connection between the light velocity shift and the scale anomaly. This study motivates the introduction of a so-called effective action charge that characterizes the velocity modifying properties of the vacuum. Several applications are given concerning vacuum modifications caused by, e.g., strong fields, Casimir systems and high temperature.Comment: 13 pages, REVTeX, 3 figures, to appear in Phys. Rev.

Quantum-critical pairing with varying exponents

We analyse the onset temperature T_p for the pairing in cuprate superconductors at small doping, when tendency towards antiferromagnetism is strong. We consider the model of Moon and Sachdev (MS), which assumes that electron and hole pockets survive in a paramagnetic phase. Within this model, the pairing between fermions is mediated by a gauge boson, whose propagator remains massless in a paramagnet. We relate the MS model to a generic \gamma-model of quantum-critical pairing with the pairing kernel \lambda (\Omega) \propto 1/\Omega^{\gamma}. We show that, over some range of parameters, the MS model is equivalent to the \gamma-model with \gamma =1/3 (\lambda (\Omega) \propto \Omega^{-1/3}). We find, however, that the parameter range where this analogy works is bounded on both ends. At larger deviations from a magnetic phase, the MS model becomes equivalent to the \gamma-model with varying \gamma >1/3, whose value depends on the distance to a magnetic transition and approaches \gamma =1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to the \gamma-model with varying \gamma <1/3. Right at the magnetic QCP, the MS model is equivalent to the \gamma-model with \gamma =0+ (\lambda (\Omega) \propto \log \Omega), which is the model for color superconductivity. Using this analogy, we verified the formula for T_c derived for color superconductivity.Comment: 10 pages, 8 figures, submitted to JLTP for a focused issue on Quantum Phase Transition

Short Strings and Gluon Propagator in the Infrared Region

We discuss how infrared region influence on short distance physics via new object, called ``short string''. This object exists in confining theories and violates the operator product expansion. Most analytical results are obtained for the dual Abelian Higgs theory, while phenomenological arguments are given for QCD.Comment: LATTICE99(confine) - 6 page

Nucleus-mediated spin-flip transitions in GaAs quantum dots

Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited states crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in $GaAs$ quantum dot.Comment: RevTex 4 pages, 1 figure, submitted to Phys. Rev.

f(R)-Brane

We investigate the existence of brane solutions in braneworld scenarios described by real scalar field in the presence of modified $f(R)$ gravity with a single extra dimension. In the case of constant curvature, we obtain first-order differential equations which solve the equations of motion and ease the search for explicit analytical solutions. Several examples of current interest are investigated to illustrate the results of the present work.Comment: 10 pages, accepted to Phys. Lett.