scholarly journals Tow kinds of Mei symmeties and conserved quantities of a mechanical system in phase space

2005 ◽  
Vol 54 (2) ◽  
pp. 500
Author(s):  
Fang Jian-Hui ◽  
Liao Yong-Pan ◽  
Peng Yong
Keyword(s):  
Phase Space ◽  
Mechanical System ◽  
Conserved Quantities

New conserved quantities of Noether–Mei symmetry of mechanical system in phase space

2008 ◽  
Vol 17 (6) ◽  
pp. 1962-1966 ◽  
Author(s):  
Fang Jian-Hui ◽  
Liu Yang-Kui ◽  
Zhang Xiao-Ni
Keyword(s):  
Phase Space ◽  
Mechanical System ◽  
Conserved Quantities ◽  
Mei Symmetry

New non-Noether conserved quantities of mechanical system in phase space

2006 ◽  
Vol 15 (10) ◽  
pp. 2197-2201 ◽  
Author(s):  
Yan Xiang-Hong ◽  
Fang Jian-Hui
Keyword(s):  
Phase Space ◽  
Mechanical System ◽  
Conserved Quantities

Noether–Lie symmetry and conserved quantities of mechanical system in phase space

2006 ◽  
Vol 15 (12) ◽  
pp. 2792-2795 ◽  
Author(s):  
Fang Jian-Hui ◽  
Liao Yong-Pan ◽  
Ding Ning ◽  
Wang Peng
Keyword(s):  
Phase Space ◽  
Mechanical System ◽  
Lie Symmetry ◽  
Conserved Quantities

Symplectic geometry of radiative modes and conserved quantities at null infinity

1981 ◽  
Vol 376 (1767) ◽  
pp. 585-607 ◽  
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Space ◽  
Degrees Of Freedom ◽  
Symplectic Geometry ◽  
Conserved Quantities ◽  
Null Infinity ◽  
Hamiltonian Description ◽  
Infinite Dimensional ◽  
Massless Spin

The Hamiltonian description of massless spin zero- and one-fields in Minkowski space is first recast in a way that refers only to null infinity and fields thereon representing radiative modes. With this framework as a guide, the phase space of the radiative degrees of freedom of the gravitational field (in exact general relativity) is introduced. It has the structure of an infinite-dimensional affine manifold (modelled on a Fréchet space) and is equipped with a continuous, weakly non-degenerate symplectic tensor field. The action of the Bondi-Metzner-Sachs group on null infinity is shown to induce canonical transformations on this phase space. The corresponding Hamiltonians – i. e. generating functions – are computed and interpreted as fluxes of supermomentum and angular momentum carried away by gravitational waves. The discussion serves three purposes: it brings out, via symplectic methods, the universality of the interplay between symmetries and conserved quantities; it sheds new light on the issue of angular momentum of gravitational radiation; and, it suggests a new approach to the quantization of the ‘true’ degrees of freedom of the gravitational field.

scholarly journals Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system

2010 ◽  
Vol 59 (6) ◽  
pp. 3639
Author(s):  
Li Yuan-Cheng ◽  
Xia Li-Li ◽  
Wang Xiao-Ming ◽  
Liu Xiao-Wei
Keyword(s):  
Mechanical System ◽  
Conserved Quantities ◽  
Mei Symmetry

QUANTUM-DEFORMED GEOMETRY ON PHASE-SPACE

1993 ◽  
Vol 08 (15) ◽  
pp. 1433-1442 ◽  
Author(s):  
E. GOZZI ◽  
M. REUTER
Keyword(s):  
Vector Field ◽  
Phase Space ◽  
Mechanical System ◽  
Time Evolution ◽  
Cotangent Bundle ◽  
Symplectic Manifolds ◽  
Hamiltonian Vector ◽  
Lie Derivative ◽  
Hamiltonian Vector Field ◽  
Quantum Analog

In this paper we extend the standard Moyal formalism to the tangent and cotangent bundle of the phase-space of any Hamiltonian mechanical system. In this manner we build the quantum analog of the classical Hamiltonian vector-field of time evolution and its associated Lie-derivative. We also use this extended Moyal formalism to develop a quantum analog of the Cartan calculus on symplectic manifolds.

Sign in / Sign up

Export Citation Format

Share Document