Results 1 to 10 of about 162 (153)

Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]

Entropy, 2020
In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
doaj   +2 more sources

Noise and Dissipation on Coadjoint Orbits. [PDF]

J Nonlinear Sci, 2018
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random attractors are found for this general class of systems when the Lie algebra is semi- simple, provided the top Lyapunov ...
Arnaudon A, De Castro AL, Holm DD.
europepmc   +7 more sources

Nonlinear flag manifolds as coadjoint orbits. [PDF]

Ann Glob Anal Geom (Dordr), 2020
AbstractA nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e ...
Haller S, Vizman C.
europepmc   +6 more sources

Adjoint and Coadjoint Orbits of the Poincaré Group [PDF]

Acta Applicandae Mathematicae, 2006
Revised arguments in section 6, results unchanged.
Richard Cushman, Cushman Richard
exaly   +4 more sources

N = (4,0) super-Liouville theory on the coadjoint orbit and PSU(1,1|2)

Physics Letters B, 2018
An N=(4,0) supersymmetric Liouville theory is formulated by the coadjoint orbit method. It is discovered that the action has symmetry under PSU(1,1|2).
Shogo Aoyama
doaj   +3 more sources

N = 4 super-Schwarzian theory on the coadjoint orbit and PSU(1,1|2)

Journal of High Energy Physics, 2018
An N = 4 super-Schwarzian theory is formulated by the coadjoint orbit method. It is discovered that the action has symmetry under PSU(1,1|2).
Shogo Aoyama, Yuco Honda
doaj   +3 more sources

Involutions in S n and associated coadjoint orbits

Journal of Mathematical Sciences, 2008
In the paper we study the coadjoint orbits of the group $\mathrm{UT}(n,K)$ associated with involutions. We obtain a formula for dimension of the orbit. We construct a polarization for the canonical element of orbit. We find a system of generators in the defining ideal of orbit.
Panov A N, A N Panov
exaly   +3 more sources

A coadjoint orbit–like construction for Jordan superalgebras

Journal of Geometry and Physics
We investigate the canonical pseudo-Riemannian metrics associated with Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan superalgebras.
Juergen Jost, Lorenz Schwachhöfer, Florio M Ciaglia   +2 more
exaly   +4 more sources

Ruang Fase Tereduksi Grup Lie Aff (1)

Jambura Journal of Mathematics, 2021
ABSTRAK Dalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine  berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari  melalui orbit coadjoint buka di titik tertentu pada ruang ...
Edi Kurniadi
doaj   +1 more source

A bound on chaos from stability

Journal of High Energy Physics, 2021
We explore the quantum chaos of the coadjoint orbit action of diffeomorphism group of S 1. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator.
Junggi Yoon
doaj   +1 more source