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The metaplectic representation and boson fields
(1991-12)
We construct explicitly the infinite-dimensional metaplectic representation and show how its use simplifies and rigorizes several questions in bosonic Quantum Field Theory. The representation permutes Gaussian elements in ...
Density functional theory on phase space
(2012)
Forty-five years after the point de départ [Hohenberg and Kohn, Phys. Rev. 1964, B864, 136] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, ...
From geometric quantization to Moyal quantization
(1995-06)
We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic ...
The Wigner transformation is of finite order
(1987-05)
The Wigner integral transformation, which intertwines the twisted product and the composition of kernels, is of order 24. Indeed, it commutes with, and its sixth power equals, the Fourier cotransformation.
Los grupos clásicos y su clasificación
(Coloquios de Matemática., 2011-08-10)
Esta es la memoria de un coloquio en la Escuela de Matemática, el 10 de agosto del 2011, en la ocasión de la visita a la UCR del Profesor Luis Joaquín Boya, de Zaragoza. Es un bosquejo de
la clasificación de los grupos ...
The Kirillov picture for the Wigner particle
(2018-06)
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincaré group, ...
Algebras of distributions suitable for phase-space quantum mechanics. III. The dual space of the algebra L_b(S)
(1989-09)
The strong dual space of the topological algebra L_b(S), where S is
the Schwartz space of smooth declining functions on R, may be obtained
as an inductive limit of projective limits of Hilbert spaces. To that
end, we ...
Dixmier traces on noncompact isospectral deformations
(2006)
We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R^l. Under deformation by a torus action, a ...
Riemannian manifolds in noncommutative geometry
(2012-07)
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, ...
The Moyal representation of quantum mechanics and special function theory
(1990-03)
It is shown that the phase-space formulation of quantum mechanics is a rich source of special function identities. The Moyal formalism is reviewed for two phase spaces: the real plane and the sphere; and this is used to ...