ar X iv : h ep - t h / 96 09 02 3 v 1 2 S ep 1 99 6 Path - Integral Aspects of Supersymmetric Quantum Mechanics ∗

ar X iv : h ep - t h / 96 09 10 9 v 1 1 2 Se p 19 96 RENORMALIZED PATH INTEGRAL IN QUANTUM MECHANICS

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick to...

ar X iv : h ep - t h / 96 07 09 3 v 1 1 2 Ju l 1 99 6 Quantum dynamics of N = 1 , D = 4 supergravity compensator

ar X iv : h ep - t h / 98 10 23 4 v 1 2 8 O ct 1 99 8 FUNCTIONAL APPROACH TO PHASE SPACE FORMULATION OF QUANTUM MECHANICS

We present BRST gauge fixing approach to quantum mechanics in phase space. The theory is obtained by ¯ h-deformation of the cohomological classical mechanics described by d = 1, N = 2 model. We use the extended phase space supplied by the path integral formulation with ¯ h-deformed symplectic structure.

ar X iv : h ep - t h / 96 02 01 3 v 1 3 F eb 1 99 6 Laughlin States on the Poincare half - plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group su q (2) symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.

ar X iv : h ep - t h / 93 09 02 9 v 1 6 S ep 1 99 3 Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial ∗

We discuss multivariable invariants of colored links associated with the N dimensional root of unity representation of the quantum group. The invariants for N > 2 are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When (N, 3) = 1 and N is odd, the invariant does not vanis...