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 ...

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 ...

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 ...

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 ...

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in ...

Este artículo apareció originalmente en la revista cultural semestral Laberintos, publicado por el Instituto de Enseñanza Superior ÉLAIOS, de Zaragoza, en un número dedicado al Año Mundial de las Matemáticas (2000). ...

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 ...

Los productos generalizados son de interés en el formalismo de la mecánica cuántica en espacios de fases. En este artículo se analizan las propiedades algebraicas y topológicas de diversos productos definidos en espacios ...

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.