Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Proceedings of the International Conference on Geometry, Integrability and Quantization
Proceedings of the International Conference on Geometry, Integrability and Quantization
Tsiganov, Andrey; Sozonov, Alexey
We consider a canonical transformation of parabolic coordinates on the plain associated with integrable
Hénon-Heiles systems and suppose that this transformation together with some additional relations may be considered as a
counterpart of the auto and hetero Bäcklund transformations.
Sako, Akifumi; Umetsu, Hiroshi
We introduce the notion of twisted Fock representations of
noncommutative Kähler manifolds and give their explicit expressions.
The so-called twisted Fock representation is a representation of the
Heisenberg like algebra whose states are constructed by acting creation
operators on a vacuum state. "Twisted" means that creation
operators are not Hermitian conjugate of annihilation operators.
In deformation quantization of Kähler manifolds
with separation of variables formulated by Karabegov, local complex
coordinates and partial derivatives of the Kähler potential with
respect to coordinates satisfy the commutation relations between
the creation and annihilation operators. Based on these relations,
the twisted Fock representation of noncommutative Kähler
manifolds is constructed.
Ryparová, Lenka; Mikeš, Josef
In this paper we study fundamental equations of
geodesics on surfaces of revolution. We obtain examples of
existence of geodesic bifurcation.
Pulov, Vladimir; Hadzhilazova, Mariana; Mladenov, Ivaïlo
The plate-ball problem concerns the shortest trajectories traced
by a rolling sphere on a horizontal plane between the prescribed
initial and final states meaning the positions and orientations of
the sphere. Here we present an explicit parametric representation
of these trajectories in terms of the Jacobian elliptic functions
and elliptic integrals.
Müller, Christian; Yasumoto, Masashi
In this paper we describe semi-discrete isothermic constant mean curvature
surfaces of revolution with smooth profile curves in Minkowski
three-space. Unlike the case of semi-discrete constant mean
curvature surfaces in Euclidean three-space, they might have
certain types of singularities in a sense defined by the second
author in a previous work. We analyze the singularities of such
surfaces.
Hinterleitner, Irena; Mikeš, Josef
In this paper we study fundamental equations of geodesic mappings
of manifolds with affine connection onto (pseudo-) Riemannian manifolds. We proved that
if a manifold with affine (or projective) connection of differentiability class $C^r (r\geq2)$
admits a geodesic mapping onto a \hbox{(pseudo-)} Riemannian manifold of class
$C^1$, then this manifold belongs to the differentiability class $C^{r+1}$.
From this result follows if an Einstein spaces admits non-trivial geodesic mappings onto (pseudo-)
Riemannian manifolds of class $C^1$ then this manifold is an Einstein space, and there exists a
common coordinate system in which the components of the metric of these Einstein manifolds are real analytic
functions.
Donchev, Veliko; Mladenova, Clementina; Mladenov, Ivaïlo
The embeddings of the $\frak{so}(3)$ Lie algebra and the Lie group
${\rm SO}(3)\)$ in higher dimensions is an important construction from
both mathematical and physical viewpoint. Here we present results based on a
program package for building the generating matrices of the irreducible embeddings of the
$\frak{so}(3)$ Lie algebra within $\frak{so}(n)$ in arbitrary dimension
$n \geq 3, n \neq 4k+2, k \in \mathbb{N}$
relying on the algorithm developed recently by Campoamor-Strursberg \cite{campoamor}.
For the remaining cases $n = 4k+2$ embeddings of $\frak{so}(3)$ into $\frak{so}(n)$ are also constructed.
Besides, we investigate the characteristic polynomials of these $\frak{so}(n)$ elements.
We show that the Cayley
map applied to $\cal{C} \in \frak{so}(n)$ is well...
Dimakis, Nikolaos
We study the existence of conservation laws in constrained systems
described by quadratic Lagrangians; the type of which is encountered in mini-superspace
cosmology. As is well known, variational symmetries lead to conserved quantities that
can be used in the classical and quantum integration of a system. Additionally - and due
to the parametrization invariance of such Lagrangians - conditional symmetries defined
on phase space can lead to non-local integrals of motion. The latter may be of importance
in various cosmological configurations. As an example we present the case of scalar field
cosmology with an arbitrary potential.
Chudá, Hana; Mikeš, Josef; Sochor, Martin
In this paper we will introduce a newly found
knowledge above the existence and the uniqueness of isoperimetric
extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds
and on surfaces on Euclidean space. We will obtain the fundamental equations
of rotary diffeomorphisms from (pseudo-) Riemannian manifolds for
twice-differentiable metric tensors onto manifolds with affine connections.
Cherevko, Yevhen; Chepurna, Olena
We studied complex and real hypersurfaces immersed in locally conformal Kähler manifolds. We have obtained
conditions for the immersions, if the manifolds admit existence of such complex hypersurfaces that are orthogonal to both Lee
and anti-Lee vector fields. Also we explore real hypersurfaces immersed in LCK-manifolds.
Brezov, Danail; Mladenova, Clementina; Mladenov, Ivaïlo
Here we develop a specific factorization technique for rotations in $\mathbb{R}^3$ into five factors about
two or three fixed axes. Although not always providing the most efficient solution, the method allows for avoiding gimbal
lock singularities and decouples the dependence on the invariant axis ${\bf n}$ and the angle $\phi$ of the compound rotation.
In particular, the solutions in the classical Euler setting are given directly by the angle of rotation $\phi$ and the
coordinates of the unit vector $\bf{n}$ without additional calculations. The immediate implementations in rigid body
kinematics are also discussed and some generalizations and potential applications in other branches of science and
technology...
Berezovskii, Volodymyr; Mikeš, Josef; Peška, Patrik
In this paper we study fundamental equations of geodesic mappings of manifolds with affine connection onto symmetric manifolds. We obtain fundamental equations of this problem.
At the end of our paper we demonstrate example of studied mappings.
Wu, Siye
We explain rich geometric structures that appear in the quantisation of
linear bosonic and fermionic systems. By contrasting with the quantisation of general curved phase spaces, we focus
on results that shed light on one of the most basic problems in quantisation:
the dependence of the quantum Hilbert space on auxiliary data such as the
choice of polarisations that is necessary to define a quantum Hilbert space.
Kisil, Vladimir
These notes describe some links between the group $\(SL_2(\mathbb{R})\)$,
the Heisenberg group and hypercomplex numbers - complex, dual and double numbers. Relations between quantum and classical mechanics
are clarified in this framework. In particular, classical mechanics can be obtained as a theory with $\emph{noncommutative}$ observables
and a $\emph{non-zero}$ Planck constant if we replace complex numbers in quantum mechanics by dual numbers. Our consideration is based on
induced representations which are build from complex$-/\-$dual$-\-/$double-valued characters. Dynamic equations, rules of additions of probabilities, ladder operators and uncertainty relations are
also discussed. Finally, we prove a Calderón--Vaillancourt-type norm estimation for relative convolutions.