The Tomita-Takesaki modular groups and conjugations for the observable algebras of space-like wedges and the vacuum state are computed for translationally covariant, but possibly not Lorentz covariant, generalized free quantum elds in arbitrary space-time dimension d. It is shown that for d 4 the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers BDFS], Lorentz...

The axiomatic formulation of quantum eld theory (QFT) of the 1950's in terms of elds deened as operator valued Schwartz distributions is reexamined in the light of subsequent developments. These include, on the physical side, the construction of a wealth of (2-dimensional) soluble QFT models with quadratic exchange relations, and, on the mathematical side, the introduction of the Colombeau alge...

The possibility of physically relevant singular solutions of the nonlinear Schrodinger equation (NLSE) with sustained dissipation into the singularity is considered through numerical study of a dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, involvi...

Quantum theory does not require the existence of discontinuities: neither in time (quantum jumps), nor in space (particles), nor in spacetime (quantum events). These apparent discontinuities are readily described objectively by the continuous process of decoherence occurring locally on a very short time scale according to the Schršdinger equation for interacting systems, while the observerÕs Ôi...

1. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on R n (n = 3) 3. Fourier inversion on R 2 4. Fourier inversion on R n (general n) 5. Fourier inversion on spheres 6. Fourier inversion on complex projective space, and variants 7. Fourier inversion on hyperbolic space, and variants 8. Fourier inversion on strongly scattering manifolds 9. Hermite expansions an...

We demonstrate the relevance of complex Gaussian stochastic processes to the stochastic state vector description of non-Markovian open quantum systems. These processes express the general Feynman-Vernon path integral propagator for open quantum systems as the classical ensemble average over stochastic pure state propagators in a natural way. They are the coloured generalization of complexWiener...

We report the rst application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the electric eld amplitude in nonlinear optical bers. We propose and study a new way to implement a global space-time adaptive grid, based on interpolation prope...

In particular, there have been studies within Supersymmetric Quantum Mechanics formalism. Cooper et al, [6], for instance, investigated the relationship between shape invariance and exactly analytical solvable potentials and showed that the Natanzon potential is not shape invariant although it has analytical solutions for the associated Schr odinger equation. L evai et al, [7], have determined...

We present a new system of modulation equations that approximate the focusing of the nonlinear Schrodinger equation in the presence of small normal time dispersion (TDNLS). Since the modulation equations are much easier for analysis and for numerical simulations, they can be used to get a general picture of the TDNLS focusing. Analytical and numerical agreement between the modulation equations...

The ared horn is modeled assuming that Webster's horn equation is satis ed. Any shape can be assumed for the wavefront within the horn. This paper presents a technique for solving Webster's horn equation as follows: The equation is converted to the form of the Schrodinger wave equation used for one-dimensional particle scattering. The horn characteristics can then be obtained directly in terms...