A method for finding complete observables in classical mechanics
Abstract
In the present work a new method for finding complete observables is discussed. In first place is presented the algorithm for systems without constraints, and in second place the method is exemplified for gauge systems. In the case of systems with first class constraints we begin with a set of clocks (non gauge invariant quantities) that are equal to the number of constraints and another non gauge invariant quantity, being all partial observables, and we finish with a gauge invariant quantity or complete observable. The starting point is to consider a partial observable and a clock or clocks being both functions of the phase space variables, that is a function of the phase space variables P(q, p) and a clock T(q, p) or clocks T1(q, p),⋯,Tn(q, p), where n is the number of first class constraint. Later, we take the equations of motion for the system and we found constants of motion and with the help of these at different times, we can find a gauge invariant phase space function associated with the partial observable P(q, p) and the set of clock or clocks.
 Publication:

XII Mexican Workshop on Particles and Fields
 Pub Date:
 September 2011
 DOI:
 10.1063/1.3622732
 Bibcode:
 2011AIPC.1361..378C
 Keywords:

 Lagrangian field theory;
 number theory;
 relativity;
 differential equations;
 11.15.Ha;
 02.10.De;
 04.25.D;
 02.60.Lj;
 Lattice gauge theory;
 Algebraic structures and number theory;
 Numerical relativity;
 Ordinary and partial differential equations;
 boundary value problems