14.2k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of WarsawPL204 papers
- Centre National de la Recherche ScientifiqueFR196 papers
- Sapienza University of RomeIT190 papers
- Max Planck Institute for Gravitational PhysicsDE187 papers
- University of PerugiaIT187 papers
- University of PisaIT185 papers
- University of Rome Tor VergataIT185 papers
- University of TrentoIT184 papers
- University of SouthamptonGB183 papers
- University of SalernoIT182 papers
- University of UrbinoIT182 papers
- Vrije Universiteit AmsterdamNL182 papers
40 papers · 1 filter
Poisson structures in the Banach setting: comparison of different approaches
Tomasz Goliński, Praful Rahangdale, Alice Barbora Tumpach
In this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them ar…
Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits
Mohammad Enayati, Jean-Pierre Gazeau, Mariano A. del Olmo +1
We elaborate the definition and properties of "massive" elementary systems in the -dimensional Anti-de Sitter (AdS) spacetime, on both classical and quantum levels. We f…
Integrable Hamiltonian systems on the symplectic realizations of
A. Odzijewicz, E. Wawreniuk
The phase space of a gyrostat with a fixed point and a heavy top is the Lie-Poisson space dual to the Lie algebra $\textbf{e}…
Some aspects of positive kernel method of quantization
Anatol Odzijewicz, Maciej Horowski
We discuss various aspects of positive kernel method of quantization of the one-parameter groups $τ_t \in \mbox{Aut}(P,\vartheta)$ of automorphisms of a -principal bundle $P(G,π…
Hamiltonian form for general autonomous ODE systems: Low dimensional examples
Artur Kobus
Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the roa…
An integrable (classical and quantum) four-wave mixing Hamiltonian system
Anatol Odzijewicz, Elwira Wawreniuk
A four-wave mixing Hamiltonian system on the classical as well as on the quantum level is investigated. In the classical case, if one assumes the frequency resonance condition of t…
Nested polyhedra and indices of orbits of Coxeter groups of non-crystallographic type
Mariia Myronova, Jiri Patera, Marzena Szajewska
The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallograp…
A family of integrable perturbed Kepler systems
Anatol Odzijewicz, Aneta Sliżewska, Elwira Wawreniuk
In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of this systems are integr…
Perturbed -Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of
Anatol Odzijewicz
We study the regularized -Kepler problem and other Hamiltonian systems which are related to the nilpotent coadjoint orbits of . The Kustaanheimo-Stiefel and Cayley…
Integrability and correspondence of classical and quantum non-linear three-mode system
A. Odzijewicz, E. Wawreniuk
The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the r…
On the Ground State Energy of the Delta-Function Fermi Gas II: Further Asymptotics
Craig A. Tracy, Harold Widom
Building on previous work of the authors, we here derive the weak coupling asymptotics to order of the ground state energy of the delta-function Fermi gas. We use a method th…
Classical and quantum Kummer shape algebras
A. Odzijewicz, E. Wawreniuk
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows fro…
Poisson Geometry Related to Atiyah Sequences
Kirill Mackenzie, Anatol Odzijewicz, Aneta Sliżewska
We construct and investigate a short exact sequence of Poisson -groupoids which is canonically related to the Atiyah sequence of a -principal bundle . Our resul…
On immanant functions related to Weyl groups of
Lenka Háková, Agnieszka Tereszkiewicz
In this work we recall the definition of matrix immanants, a generalization of the determinant and permanent of a matrix. We use them to generalize families of symmetric and antisy…
Generalized discrete orbit function transforms of affine Weyl groups
Tomasz Czyżycki, Jiří Hrivnák
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the…
Lie bundle on the space of deformed skew-symmetric matrices
Alina Dobrogowska, Tomasz Goliński
We study a Lie algebra of deformed skew-symmetric matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix.…
Coherent states and quantum numbers for twist-deformed oscillator model
Marcin Daszkiewicz, Cezary J. Walczyk
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled…
Integrable Systems Related to Deformed
Alina Dobrogowska, Anatol Odzijewicz
We investigate a family of integrable Hamiltonian systems on Lie-Poisson spaces dual to Lie algebras being two-parameter deformations o…
Cohomological resolutions for anomalous Lie constraints
Zbigniew Hasiewicz, Cezary J. Walczyk
It is shown that the BRST resolution of the spaces of physical states of the systems with anomalies can be consistently defined. The appropriate anomalous complexes are obtained by…
Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2
Francis W. Lemire, Jiri Patera, Marzena Szajewska
The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining pr…
Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling
Alina Dobrogowska, Anatol Odzijewicz
In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit couplin…
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
Anatol Odzijewicz, Tomasz Goliński
In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for so…
Four types of special functions of G_2 and their discretization
Marzena Szajewska
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (cal…
Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal
Anatol Odzijewicz, Alina Dobrogowska
By application of the coinduction method as well as Magri method to the ideal of real Hilbert-Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on th…