2 8 M ay 2 00 4 Integrable quadratic Hamiltonians on so ( 4 ) and so ( 3 , 1 ) Vladimir
نویسندگان
چکیده
In this paper we consider the following family of Poisson brackets {Mi,Mj} = εijk Mk, {Mi, γj} = εijk γk, {γi, γj} = κ εijk Mk. (1.1) Here Mi and γi are components of 3-dimensional vectors M and Γ, εijk is the totally skew-symmetric tensor, κ is a parameter. It is well-known that any linear Poisson bracket is defined by an appropriate Lie algebra. The cases κ = 0, κ > 0 and κ < 0 correspond to the Lie algebras e(3), so(4) and so(3, 1). In this paper we assume κ 6= 0.
منابع مشابه
2 8 M ay 2 00 4 Integrable quadratic Hamiltonians on so ( 4 ) and so ( 3 , 1 )
In this paper we consider the following family of Poisson brackets {Mi,Mj} = εijk Mk, {Mi, γj} = εijk γk, {γi, γj} = κ εijk Mk. (1.1) Here Mi and γi are components of 3-dimensional vectors M and Γ, εijk is the totally skew-symmetric tensor, κ is a parameter. It is well-known that any linear Poisson bracket is defined by an appropriate Lie algebra. The cases κ = 0, κ > 0 and κ < 0 correspond to ...
متن کاملIntegrable quadratic classical Hamiltonians on so(4) and so(3, 1)
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree. PACS numbers: 02.30.Hq, 02.30.Ik, 45.30.+s Mathematics Subject Classification: 34M55, 37J35, 37N15
متن کاملO ct 2 00 1 A generalized Kowalevski Hamiltonian and new integrable cases on e ( 3 ) and so ( 4 ) . Vladimir
A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,
متن کاملep - l at / 0 10 50 07 v 1 8 M ay 2 00 1 Fermion propagator at finite temperatures on extremely anisotropic lattice . Vladimir
Fermion propagator is computed in a simple model on an extremely anisotropic lattice ξ ≫ 1. Fermion determinant is evaluated up to ξ−4 order. Chiral condensate is estimated in mean field approximation.
متن کاملar X iv : m at h - ph / 0 00 50 19 v 1 1 6 M ay 2 00 0 2 and 3 - dimensional Hamiltonians with Shape Invariance Symmetry
Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008