93 research outputs found
On the Obstructions to non-Cliffordian Pin Structures
We derive the topological obstructions to the existence of non-Cliffordian
pin structures on four-dimensional spacetimes. We apply these obstructions to
the study of non-Cliffordian pin-Lorentz cobordism. We note that our method of
derivation applies equally well in any dimension and in any signature, and we
present a general format for calculating obstructions in these situations.
Finally, we interpret the breakdown of pin structure and discuss the relevance
of this to aspects of physics.Comment: 31 pages, latex, published in Comm. Math. Phys. 164, No. 1, pages
65-87 (1994
A C*-Algebraic Model for Locally Noncommutative Spacetimes
Locally noncommutative spacetimes provide a refined notion of noncommutative
spacetimes where the noncommutativity is present only for small distances. Here
we discuss a non-perturbative approach based on Rieffel's strict deformation
quantization. To this end, we extend the usual C*-algebraic results to a
pro-C*-algebraic framework.Comment: 13 pages, LaTeX 2e, no figure
The Absolute Line Quadric and Camera Autocalibration
We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques
The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach
A symplectic theory approach is devised for solving the problem of
algebraic-analytical construction of integral submanifold imbeddings for
integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on
canonically symplectic phase spaces
In-situ epitaxial growth of superconducting La-based bilayer cuprate thin films
We investigate the epitaxial growth of bilayer cuprate La2CaCu2O6+\delta
using pure ozone as an oxidant, and find that even the crystal with parent
composition without cation substitution can show metallic behavior with the aid
of epitaxial strain effect. The hole concentration is controlled simply by
excess-oxygen doping, and the films grown under the optimum conditions exhibit
superconductivity below 30 K. This is the first result on the superconductivity
of bilayer La2CaCu2O6+\delta induced purely by the excess oxygen.Comment: 5 pages, 3 figures, To appear in Phys. Rev. B, Rapid Communication
Virtually abelian K\"ahler and projective groups
We characterise the virtually abelian groups which are fundamental groups of
compact K\"ahler manifolds and of smooth projective varieties. We show that a
virtually abelian group is K\"ahler if and only if it is projective. In
particular, this allows to describe the K\"ahler condition for such groups in
terms of integral symplectic representations
Toeplitz Quantization of K\"ahler Manifolds and
For general compact K\"ahler manifolds it is shown that both Toeplitz
quantization and geometric quantization lead to a well-defined (by operator
norm estimates) classical limit. This generalizes earlier results of the
authors and Klimek and Lesniewski obtained for the torus and higher genus
Riemann surfaces, respectively. We thereby arrive at an approximation of the
Poisson algebra by a sequence of finite-dimensional matrix algebras ,
.Comment: 17 pages, AmsTeX 2.1, Sept. 93 (rev: only typos are corrected
N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces
We study a topological Yang-Mills theory with fermionic symmetry. Our
formalism is a field theoretical interpretation of the Donaldson polynomial
invariants on compact K\"{a}hler surfaces. We also study an analogous theory on
compact oriented Riemann surfaces and briefly discuss a possible application of
the Witten's non-Abelian localization formula to the problems in the case of
compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in
Comm. Math. Phy
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
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