882 research outputs found
Star Products on Coadjoint Orbits
We study properties of a family of algebraic star products defined on
coadjoint orbits of semisimple Lie groups. We connect this description with the
point of view of differentiable deformations and geometric quantization.Comment: Talk given at the XXIII ICGTMP, Dubna (Russia) August 200
On invariants of almost symplectic connections
We study the irreducible decomposition under Sp(2n, R) of the space of
torsion tensors of almost symplectic connections. Then a description of all
symplectic quadratic invariants of torsion-like tensors is given. When applied
to a manifold M with an almost symplectic structure, these instruments give
preliminary insight for finding a preferred linear almost symplectic connection
on M . We rediscover Ph. Tondeur's Theorem on almost symplectic connections.
Properties of torsion of the vectorial kind are deduced
Phase Space Reduction for Star-Products: An Explicit Construction for CP^n
We derive a closed formula for a star-product on complex projective space and
on the domain using a completely elementary
construction: Starting from the standard star-product of Wick type on and performing a quantum analogue of Marsden-Weinstein
reduction, we can give an easy algebraic description of this star-product.
Moreover, going over to a modified star-product on ,
obtained by an equivalence transformation, this description can be even further
simplified, allowing the explicit computation of a closed formula for the
star-product on \CP^n which can easily transferred to the domain
.Comment: LaTeX, 17 page
Identification of Berezin-Toeplitz deformation quantization
We give a complete identification of the deformation quantization which was
obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler
manifold. The deformation quantization with the opposite star-product proves to
be a differential deformation quantization with separation of variables whose
classifying form is explicitly calculated. Its characteristic class (which
classifies star-products up to equivalence) is obtained. The proof is based on
the microlocal description of the Szegoe kernel of a strictly pseudoconvex
domain given by Boutet de Monvel and Sjoestrand.Comment: 26 page
A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces
Let be a simply connected spin compact inner irreducible symmetric
space, endowed with the metric induced by the Killing form of sign-changed.
We give a formula for the square of the first eigenvalue of the Dirac operator
in terms of a root system of . As an example of application, we give the
list of the first eigenvalues for the spin compact irreducible symmetric spaces
endowed with a quaternion-K\"{a}hler structure
Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for \complex \mbox{\LARGE P}^n
Based on a closed formula for a star product of Wick type on \CP^n, which
has been discovered in an earlier article of the authors, we explicitly
construct a subalgebra of the formal star-algebra (with coefficients contained
in the uniformly dense subspace of representative functions with respect to the
canonical action of the unitary group) that consists of {\em converging} power
series in the formal parameter, thereby giving an elementary algebraic proof of
a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this
subalgebra the formal parameter can be substituted by a real number :
the resulting associative algebras are infinite-dimensional except for the case
, a positive integer, where they turn out to be isomorphic to
the finite-dimensional algebra of linear operators in the th energy
eigenspace of an isotropic harmonic oscillator with degrees of freedom.
Other examples like the -torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font
Twistor theory of symplectic manifolds
This article is a contribution to the understanding of the geometry of the
twistor space of a symplectic manifold. We consider the bundle with fibre
the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold
M. Then, after recalling the construction of the almost complex structure
induced on by a symplectic connection on M, we study and find some specific
properties of both. We show a few examples of twistor spaces, develop the
interplay with the symplectomorphisms of M, find some results about a natural
almost Hermitian structure on and finally prove its n+1-holomorphic
completeness. We end by proving a vanishing theorem about the Penrose
transform.Comment: 34 page
Integral closure of rings of integer-valued polynomials on algebras
Let be an integrally closed domain with quotient field . Let be a
torsion-free -algebra that is finitely generated as a -module. For every
in we consider its minimal polynomial , i.e. the
monic polynomial of least degree such that . The ring consists of polynomials in that send elements of back to
under evaluation. If has finite residue rings, we show that the
integral closure of is the ring of polynomials in which
map the roots in an algebraic closure of of all the , ,
into elements that are integral over . The result is obtained by identifying
with a -subalgebra of the matrix algebra for some and then
considering polynomials which map a matrix to a matrix integral over . We
also obtain information about polynomially dense subsets of these rings of
polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix,
integral closure, pullback, polynomially dense set. accepted for publication
in the volume "Commutative rings, integer-valued polynomials and polynomial
functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201
Parallelisable Heterotic Backgrounds
We classify the simply-connected supersymmetric parallelisable backgrounds of
heterotic supergravity. They are all given by parallelised Lie groups admitting
a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14
and 16 of the 16 supersymmetries.Comment: 17 pages, AMSLaTe
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