3,409 research outputs found
Projectively and conformally invariant star-products
We consider the Poisson algebra S(M) of smooth functions on T^*M which are
fiberwise polynomial. In the case where M is locally projectively (resp.
conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.
SO(p+1,q+1))-invariant. We prove the existence of such star-products using the
projectively (resp. conformally) equivariant quantization, then prove their
uniqueness, and study their main properties. We finally give an explicit
formula for the canonical projectively invariant star-product.Comment: 37 pages, Latex; minor correction
Representations of the conformal Lie algebra in the space of tensor densities on the sphere
Let be the space of tensor densities on
of degree . We consider this space as an induced module
of the nonunitary spherical series of the group and
classify -sim{\mathcal F}_\lambda(\mathbb{S}^n)\lambda$.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP
Inelastic light, neutron, and X-ray scatterings related to the heterogeneous elasticity of glasses
The effects of plasticization of poly(methyl methacrylate) glass on the boson
peaks observed by Raman and neutron scattering are compared. In plasticized
glass the cohesion heterogeneities are responsible for the neutron boson peak
and partially for the Raman one, which is enhanced by the composition
heterogeneities. Because the composition heterogeneities have a size similar to
that of the cohesion ones and form quasiperiodic clusters, as observed by small
angle X-ray scattering, it is inferred that the cohesion heterogeneities in a
normal glass form nearly periodic arrangements too. Such structure at the
nanometric scale explains the linear dispersion of the vibrational frequency
versus the transfer momentum observed by inelastic X-ray scattering.Comment: 9 pages, 2 figures, to be published in J. Non-Cryst. Solids
(Proceedings of the 4th IDMRCS
Non-Commutative Corrections to the MIC-Kepler Hamiltonian
Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in
the presence of a magnetic monopole) are computed in Cartesian and parabolic
coordinates. Despite the fact that there is no simple analytic expression for
non-commutative perturbative corrections to the MIC-Kepler spectrum, there is a
term that gives rise to the linear Stark effect which didn't exist in the
standard hydrogen model.Comment: 5 page
Conformally equivariant quantization: Existence and uniqueness
We prove the existence and the uniqueness of a conformally equivariant symbol
calculus and quantization on any conformally flat pseudo-Riemannian manifold
(M,\rg). In other words, we establish a canonical isomorphism between the
spaces of polynomials on and of differential operators on tensor
densities over , both viewed as modules over the Lie algebra \so(p+1,q+1)
where . This quantization exists for generic values of the weights
of the tensor densities and compute the critical values of the weights yielding
obstructions to the existence of such an isomorphism. In the particular case of
half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio
Transverse Shifts in Paraxial Spinoptics
The paraxial approximation of a classical spinning photon is shown to yield
an "exotic particle" in the plane transverse to the propagation. The previously
proposed and observed position shift between media with different refractive
indices is modified when the interface is curved, and there also appears a
novel, momentum [direction] shift. The laws of thin lenses are modified
accordingly.Comment: 3 pages, no figures. One detail clarified, some misprints corrected
and references adde
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Let be an odd-dimensional Euclidean space endowed with a contact 1-form
. We investigate the space of symmetric contravariant tensor fields on
as a module over the Lie algebra of contact vector fields, i.e. over the
Lie subalgebra made up by those vector fields that preserve the contact
structure. If we consider symmetric tensor fields with coefficients in tensor
densities, the vertical cotangent lift of contact form is a contact
invariant operator. We also extend the classical contact Hamiltonian to the
space of symmetric density valued tensor fields. This generalized Hamiltonian
operator on the symbol space is invariant with respect to the action of the
projective contact algebra . The preceding invariant operators lead
to a decomposition of the symbol space (expect for some critical density
weights), which generalizes a splitting proposed by V. Ovsienko
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