Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

Families of superintegrable Hamiltonians constructed from exceptional polynomials

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable

Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold

We investigate an operator ordering problem in two-dimensional N=1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.Comment: 7 page

Pion and Kaon Electromagnetic Form Factors

We study the electromagnetic form factor of the pion and kaons at low-energies with the use of Chiral Perturbation Theory. The analysis is performed within the three flavour framework and at next-to-next-to-leading order. We explain carefully all the relevant consistency checks on the expressions, present full analytical results for the pion form factor and describe all the assumptions in the analysis. From the phenomenological point of view we make use of our expression and the available data to obtain the charge radius of the pion obtaining $_V^\pi=(0.452+-0.013) fm^2$, as well as the low-energy constant $L_9^r(m_\rho)= (5.93+-0.43)10^{-3}$. We also obtain experimental values for 3 combinations of order $p^6$ constants.Comment: 50 page

Convergence of resonances on thin branched quantum wave guides

We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family X_\eps of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on X_\eps approximate those of the Laplacian with ``free'' boundary conditions on $X_0$, the skeleton graph of X_\eps.Comment: 48 pages, 1 figur

Crohn's disease activity index and Vienna classification - Is it worthwhile to calculate before surgery?

Background: Crohn's disease (CD) patients with increased disease activity may reveal an increased risk for perioperative complications. The `Crohn's disease activity index' (CDAI) and the `Vienna classification' (VC) were developed for standardized disease activity estimations. The significance of these scores to predict extent, type and early outcome of surgery in CD patients was analyzed. Methods: In 179 surgically treated CD patients, the CDAI and VC were assessed from a prospective database. Relations of the scores with CD risk factors, type, number, location and complications of surgery were analyzed. Results: VC behavior and location subtypes were associated with distinct types of surgery (i.e. `strictureplasty' in `stricturing disease', `colon surgery' in `colon involvement'), but not with surgery type and extent or outcome. Surgery extent (i.e. with 5 vs. 3 `surgical sites' 425 +/- 25 vs. 223.3 +/- 25) and complications (357.1 +/- 36.9 (with) vs. 244.4 +/- 13 (without)) were associated with elevated CDAI levels; however, nicotine abuse remained the only significant risk factor for perioperative complications after multiple logistic regression. Conclusion: The significance of VC or CDAI for predicting the extent of surgery or complications is limited. None of the tested variables except preoperative nicotine abuse influenced the likelihood for perioperative complications. Copyright (c) 2006 S. Karger AG, Base