Renormalization Group in Quantum Mechanics

The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The hamiltonian and the lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models.Comment: Updated and extended version to appear in Annals of Physics, 24pg, TEX fil

Path Integral for the Dirac Equation

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.Comment: 5 pages, revtex. Argument extended, several equations corrected, more references adde

Self-Quenched Dynamics

We introduce a model for the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by the landscape itself. By choosing relevant measures of time and potential this self-quenched dynamics can be mapped on to the ``True'' Self-Avoiding Walk model. This correspondence reveals that the average distance of the walker at time $t$ from its starting point is $R(t)\sim\log(t)^\gamma$, where $\gamma=2/3$ for one dimension and 1/2 for all higher dimensions. Furthermore, the evolution of the landscape is similar to that in growth models with extremal dynamics.Comment: svjour,epj 5 pages including 4 figure