Difficulties with massless particles?

Some difficulties with sharp momentum (one-particle) states for massless particles are indicated, in the framework of unitary irreducible representations of the Poincaré group. It is shown that a Poincaré covariant set of such states requires the introduction, in the spatial direction opposite to the point stabilized, of momentum generalized eigenstates which (when the helicity is nonzero) have a nontrivial orbital transformation. The relevance of these generalized momentum eigenstates for massless theories is then shown.     

Fine structure inversion of the 3d excited state of sodium

The observed inversion of the fine structure of the excited 3d state of the sodium atom explained as due to a second-order effect between the electrostatic dipole exchange interaction and the magnetic spin-orbit interaction acting on the core 2p electrons.     

Some Infinite-Dimensional Algebras Arising in Spin Systems and in Particle Physics and their Grand Algebra

We indicate similarities in the structure of two types of infinite-dimensional algebras, one introduced 28 years ago in connection with the mass problem of elementary particles and the other seven years ago in connection with spin systems (XY models). We show that these algebras can be considered as representations of a single Grand Algebra, the enveloping algebra of an affine Kac–Moody algebra built on the Poincaré Lie algebra. As an associative and coassociative bialgebra of operators, the latter representation of the grand algebra is a preferred nontrivial deformation of the Ising case bialgebra.     

Do different deformations lead to the same spectrum?

The procedure of 1 quantization introduces the notions of mathematical equivalence and of 1 spectrum. We prove that mathematical equivalence, as a change of ordering for quantum operators to which it is related, does not preserve 1 spectrum unless it reduces to an automorphism of the 1 product. Suggestions about the 《correct》 choice of 1 products are made.     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

Some reflections on mathematicians’ views of quantization

We start with a short presentation of the difference in attitude between mathematicians and physicists even in their treatment of physical reality, and look at the paradigm of quantization as an illustration. In particular, we stress the differences in motivation and realization between the Berezin and deformation quantization approaches, exposing briefly Berezin’s view of quantization as a functor. We continue with a schematic overview of deformation quantization and of its developments in contrast with the latter and discuss related issues, in particular, the spectrality question. We end by a very short survey of two main avatars of deformation quantization, quantum groups and quantum spaces (especially noncommutative geometry) presented in that perspective. Bibliography: 74 titles. This paper is dedicated to the memory of “Alik” Berezin Published in Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 199–220.     

Theory of nuclear quadrupole interactions in ionic iron-group compounds—Role of antishielding effects

Hyperfine Interactions -     

Croissance hors des singularités de séries de Dirichlet,et applications

Résumé En vue d'étudier la forme des transformées de Fourier d'une classe de fonctions entières on est amené, d'après un théorème de S. Mandelbrojt, à construire certaines séries de Dirichlet, et à en évaluer de fa?on précise la croissance hors des singularités—la forme étant d'autant mieux cernée que l'évaluation aura été plus précise. On obtient également un théorème de composition des singularités, notamment pour les séries de Dirichlet ayant la croissance (au plus de type exponentiel minimal) considérée.     

Deformation theory applied to quantization and statistical mechanics

After a review of the deformation (star product) approach to quantization, treated in an autonomous manner as a deformation (with parameter ) of the algebraic composition law of classical observables on phase-space, we show how a further deformation (with parameter ) of that algebra is suitable for statistical mechanics. In this case, the phase-space is endowed with what we call a conformal symplectic (or conformal Poisson) structure, for which the bracket is the Poisson bracket modified by terms of order (1, 0) and (0, 1). As an application, one sees that the KMS states (classical or quantum) are those that vanish on the modified (Poisson or Moyal-Vey) bracket of any two observables, multiplied by a conformal factor.