A Quantum Exactly Solvable Nonlinear Oscillator with quasi-Harmonic Behaviour

The quantum version of a non-linear oscillator, previouly analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form $m={(1+\lambda x^2)}^{-1}$ and with a \la-dependent nonpolynomial rational potential. This \la-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for \la\to 0 all the characteristics of the linear oscillator are recovered. Firstly, the \la-dependent Schr\"odinger equation is exactly solved as a Sturm-Liouville problem and the \la-dependent eigenenergies and eigenfunctions are obtained for both \la>0 and \la<0. The \la-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as \la-deformations of the standard Hermite polynomials. In the second part, the \la-dependent Schr\"odinger equation is solved by using the Schr\"odinger factorization method, the theory of intertwined Hamiltonians and the property of shape invariance as an approach. Finally, the new family of orthogonal polynomials is studied. We prove the existence of a \la-dependent Rodrigues formula, a generating function and \la-dependent recursion relations between polynomials of different orders.Comment: 29 pages, 4 figure

Chern-Simons Theory, Colored-Oriented Braids and Link invariants

A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators of $SU(2)_k$ Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicitly calculated as illustrations for knots upto eight crossings and two-component multicoloured links upto seven crossings.Comment: 48 pages + 20 diagram

Lattice Chern-Simons Gravity via Ponzano-Regge Model

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.Comment: LaTeX, 26 pages, 6 eps figure

Does Political Ambiguity Pay? Corporate Campaign Contributions and the Rewards to Legislator Reputation

Do politicians tend to follow a strategy of ambiguity in their policy positions or a strategy of reputational development to reduce uncertainty about where they stand? Ambiguity could allow a legislator to avoid alienating constituents and to play rival interests off against each other to maximize campaign contributions. Alternatively, reputational clarity could help to reduce uncertainty about a candidate and lead to high campaign contributions from favored interests. We outline a theory that considers conditions under which a politician would and would not prefer reputational development and policy-stance clarity in the context of repeat dealing with special interests. Our proxy for reputational development is the percent of repeat givers to a legislator. Using data on corporate political action committee contributions (PACs) to members of the U.S. House during the seven electoral cycles from 1983/84 to 1995/96, we find that legislators do not appear to follow a strategy of ambiguity and that high reputational development is rewarded with high PAC contributions.

Homotopy locally presentable enriched categories

We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for simplicially-enriched categories, links homotopy locally presentable V-categories with combinatorial model V-categories, in the case where has all objects of V are cofibrant.Comment: 48 pages. Significant changes in v2, especially in the last sectio