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A nonperturbative form of the spectral action principle in noncommutative geometry
(1998-07)
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 ...
Improved Epstein-Glaser renormalization in x-space versus differential renormalization
(2014-09)
Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This ...
Algebras of distributions suitable for phase‐space quantum mechanics. II. Topologies on the Moyal algebra
(1988-06-04)
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 ...
The local index formula for SU_q(2)
(2005)
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 ...
Testing one-body density functionals on a solvable model
(2012-10)
There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the ...
On the ultraviolet behaviour of quantum fields over noncommutative manifolds
(1999-03)
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 ...
El problema de los subespacios invariantes
(1983-11)
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 ...
Connes' tangent groupoid and strict quantization
(1999-12)
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 ...
Examples of noncommutative geometrical spaces
(2004-01)
We develop some examples of spectral triples in noncommutative geometry, on the theme of the noncommutative torus but with several variations.
Algunas fórmulas útiles para productos torcidos
(1986)
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 ...