67 research outputs found
A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces
The usual Weyl calculus is intimately associated with the choice of the
standard symplectic structure on . In this
paper we will show that the replacement of this structure by an arbitrary
symplectic structure leads to a pseudo-differential calculus of operators
acting on functions or distributions defined, not on but
rather on . These operators are intertwined
with the standard Weyl pseudo-differential operators using an infinite family
of partial isometries of \ indexed by . This allows
us obtain spectral and regularity results for our operators using Shubin's
symbol classes and Feichtinger's modulation spaces.Comment: 32 pages, latex file, published versio
The singularity problem and phase-space noncanonical noncommutativity
The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is
considered for a Schwarzschild black hole under the assumption that the scale
factors and the associated momenta satisfy a noncanonical noncommutative
extension of the Heisenberg-Weyl algebra. An integral of motion is used to
factorize the wave function into an oscillatory part and a function of a
configuration space variable. The latter is shown to be normalizable using
asymptotic arguments. It is then shown that on the hypersufaces of constant
value of the argument of the wave function's oscillatory piece, the probability
vanishes in the vicinity of the black hole singularity.Comment: 4 pages, revtex
Reflecting boundaries and massless factorized sattering in to dmensions
This thesis is concerned with two-dimensional models that are integrable in the presence of a boundary and whose spectrum in the bulk is constituted of massless particles. Although there is already a vast literature on the subject (e.g. Kondo and Callan-Rubakov models), the common minimal denominator in all these situations is the fact that the bulk theory is conformal invariant and it is the boundary that is responsible for the broken scale invariance. Here, our purpose is to consider the alternative situation, where the boundary respects the conformal invariance of the theory and the renormalization group trajectory is controlled by a bulk perturbation. The model in question is the principal chiral model at level k = 1. We propose the set of permissible boundary conditions suggested by the symmetries of the problem and compute the corresponding minimal reflection matrices. For one of the boundary conditions we compute the boundary ground state energy and the boundary entropy using the technique of boundary thermodynamic Bethe ansatz. In the infrared limit our results are shown to be in complete agreement with the predictions of the boundary conformal field theory approach. Finally, we consider the classical supersymmetric Liouville theory on the half-line and compute the boundary conditions compatible with the superconformal invariance. We construct an infinite set of commuting integrals of motion using Lax-pair techniques and discuss some aspects of the quantum theory as well as its relation to the super Korteweg-de Vries equation
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