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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 ...
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 ...
Connes' noncommutative differential geometry and the Standard Model
(1993-11)
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 ...
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 ...
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 ...
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 ...
Los grupos simplécticos y su representación en la teoría del producto cuántico. I. Sp(2,R)
(1987)
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 ...
Quadratic Hamiltonians in phase-space quantum mechanics
(1989-07)
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 ...
Algebras of distributions suitable for phase‐space quantum mechanics. I
(1988-06-04)
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 ...
S-matrix from the metaplectic representation
(1992-03)
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.