The topology of the Moyal *-algebra may be defined in three ways: the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space ...

By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields described by Connes' axioms for noncommutative ...

In this paper, the Connes-Lott approach to the phenomenological Lagrangian of the standard theory of elementary particles is reviewed in detail. The paper is self-contained, in that the necessary foundations in noncommutative ...

Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein ...

Investigamos dos modificaciones del producto cuántico o torcido de funciones sobre el espacio de fases, y proporcionamos una colección de fórmulas útiles en el cálculo con estos productos. La primera modificación es la ...

We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby ...

El álgebra de observables de la teoría cuántica encierra una representación del grupo simpléctico. Esta puede usarse a su vez para resolver problemas de caracterización de estados y síntesis espectral en la formulación ...

The dynamical evolution is described within the phase-space formalism by means of the Moyal propagator, which is the symbol of the evolution operator. Quadratic Hamiltonians on the phase space are distinguished in that ...

The twisted product of functions on R^2N is extended to a *-algebra of tempered distributions which contains the rapidly decreasing smooth functions, the distributions of compact support, and all polynomials, and moreover ...

We show how the S-matrix for bosons in an external field can be derived directly from the infinite dimensional metaplectic representation, in terms of the classical scattering operator.