Phase space representations of the Poincaré group & their applications to relativistic particle dynamics

1979 ◽  
pp. 184-185
Author(s):  
S. Twareque Ali ◽  
E. Prugovečki
Keyword(s):  
Phase Space ◽  
Relativistic Particle ◽  
Particle Dynamics ◽  
Poincaré Group ◽  
Poincare Group

IRREVERSIBILITY IN CLASSICAL MECHANICS AS A CONSEQUENCE OF POINCARÉ GROUP

1996 ◽  
Vol 10 (21) ◽  
pp. 2675-2685 ◽  
Author(s):  
I. P. PAVLOTSKY ◽  
M. STRIANESE
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
Poincaré Group ◽  
Singular Surfaces ◽  
Poincare Group ◽  
Galilei Group ◽  
Local Singularity ◽  
Molecular Potentials ◽  
Dynamical Properties ◽  
Infinite Set

In the post-Galilean approximation of Poincaré Group (i.e. in the approximation in which the corrections of order O (c−2), c denoting the light velocity, to the Galilei group are taken in account) the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces.1–4 In particular, on some submanifolds of the singular manifold the velocities are not determined uniquely: in each point of the submanifold we get the infinite set of components of velocity. It means the loss of the reversibility of the motion in a sense that transformation of the phase space, corresponding to Lagrangian, has not a property of a group. It is shown, that if the values of the derivates of the molecular potentials are large enough the irreversibility of motion takes place. As consequence we obtain the relaxation to the equilibrium. This property does not exist if the Lagrangian is invariant with respect to Galilei Group.

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