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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 ...
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 ...
Quantum electrodynamics in external fields from the spin representation
(1994-07)
Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in quantum field theory. This representation permutes "Gaussian" elements in the fermion Fock space, and is necessarily ...
On the kinematics of the last Wigner particle
(2019)
Wigner's particle classification provides for "continuous spin" representations of the Poincaré group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by ...
Nonnegative mixed states in Weyl–Wigner–Moyal theory
(1988-03-21)
We classify the gaussian Wigner functions corresponding to mixed states and show that, unlike the case of pure states, not all nonnegative mixed states are gaussian.
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 ...
Quantum gauge models without classical Higgs mechanism
(2010-09-15)
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 ...
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 ...