As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent ...

El Prof. Carl Pearcy, de la Universidad de Michigan en Ann Arbor, visitó la Escuela de Matemática en noviembre de 1983, y ofreció un minicurso de tres sesiones sobre el problema de los subespacios invariantes. Dicho problema ...

A formalism is proposed for developing phase-space representations of elementary quantum systems under general invariance groups. Several examples are discussed, including the usual Weyl calculus, the Moyal formulation ...

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.

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 develop some examples of spectral triples in noncommutative geometry, on the theme of the noncommutative torus but with several variations.

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 discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as ...

For a renormalizability proof of perturbative models in the Epstein-Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction ...