Exact solutions of the Dirac equation and induced representations of the Poincare group on the lattice

We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincare group on the lattice reveals that they are reducible, a result that can be considered a group theoretical approach to the problem of fermion doubling.Comment: LaTeX, 4 pages, (late submission

Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom

The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.Comment: LaTeX, 14 pages (late submission

Integrable systems on the lattice and orthogonal polynomials of discrete variable

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.Comment: LaTeX, 10 pages, Comunication presented to the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications, Rome, June 2001 (late submission to arxiv.org