On a 2N dimensional phase space, consider the set of functions which are purely quadratic in...

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On a 2N dimensional phase space, consider the set of functions which are purely quadratic in the generalised coordinates and momenta. (a) Show that the Poisson bracket of any two members of the set is again in the set. (b) Let the Hamiltonian be given by, H (p + q?) = i=1 which functions in the above set constitute infinitesimal symmetries of the system? How many independent symmetries are there? On a 2N dimensional phase space, consider the set of functions which are purely quadratic in the generalised coordinates and momenta. (a) Show that the Poisson bracket of any two members of the set is again in the set. (b) Let the Hamiltonian be given by, H (p + q?) = i=1 which functions in the above set constitute infinitesimal symmetries of the system? How many independent symmetries are there?