51 research outputs found
Symmetric Spaces and Star representations II : Causal Symmetric Spaces
We construct and identify star representations canonically associated with
holonomy reducible simple symplectic symmetric spaces. This leads the a
non-commutative geometric realization of the correspondence between causal
symmetric spaces of Cayley type and Hermitian symmetric spaces of tube type.Comment: 13 page
Non-formal deformation quantizations of solvable Ricci-type symplectic symmetric spaces
Ricci-type symplectic manifolds have been introduced and extensively studied
by M. Cahen et al.. In this note, we describe their deformation quantizations
in the split solvable symmetric case. In particular, we introduce the notion of
non-formal tempered deformation quantization on such a space. We show that the
set of tempered deformation quantizations is in one-to-one correspondence with
the space of Schwartz operator multipliers on the real line. Moreover we prove
that every invariant formal star product on a split Ricci-type solvable
symmetric space is an asymptotic expansion of a tempered non-formal
quantization. This note illustrates and partially reviews through an example a
problematic studied by the author regarding non-formal quantization in presence
of large groups of symmetries
Regular Poisson structures on massive non-rotating BTZ black holes
We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian
symmetric space context. Using classical symmetric space techniques we find
that every such space intrinsically carries a regular Poisson structure whose
symplectic leaves are para-hermitian symmetric surfaces. We also obtain a
global expression of the metric yielding a dynamical description of the black
hole from its initial to its final singularity.Comment: LaTex, 18 pages, 3 figures, version published in Nucl. Phys.
Global geometry of the 2+1 rotating black hole
The generic rotating BTZ black hole, obtained by identifications in AdS3
space through a discrete subgroup of its isometry group, is investigated within
a Lie theoretical context. This space is found to admit a foliation by
two-dimensional leaves, orbits of a two-parameter subgroup of SL(2,R) and
invariant under the BTZ identification subgroup. A global expression for the
metric is derived, allowing a better understanding of the causal structure of
the black hole.Comment: 9 pages, 1 figur
The deformation quantizations of the hyperbolic plane
We describe the space of (all) invariant deformation quantizations on the
hyperbolic plane as solutions of the evolution of a second order hyperbolic
differential operator. The construction is entirely explicit and relies on
non-commutative harmonic analytical techniques on symplectic symmetric spaces.
The present work presents a unified method producing every quantization of the
hyperbolic plane, and provides, in the 2-dimensional context, an exact solution
to Weinstein's WKB quantization program within geometric terms. The
construction reveals the existence of a metric of Lorentz signature canonically
attached (or `dual') to the geometry of the hyperbolic plane through the
quantization process.Comment: 26 pages, 5 figure
Deformations of quantum field theories on de Sitter spacetime
Quantum field theories on de Sitter spacetime with global U(1) gauge symmetry
are deformed using the joint action of the internal symmetry group and a
one-parameter group of boosts. The resulting theory turns out to be wedge-local
and non-isomorphic to the initial one for a class of theories, including the
free charged Dirac field. The properties of deformed models coming from
inclusions of CAR-algebras are studied in detail.Comment: 26 pages, no figure
- …