Three-particle relativistic harmonic dynamics in the constraint formalism

Three-particle relativistic harmonic dynamics in the constraint formalism has been studied in two different schemes for the reduction of the 24-dimensional covariant phase space to an 18-dimensional minimum phase space. Three-body potential for the harmonic problem has been determined from the Bidikov-Todorov equation. It is found that the classical equations of motion are separable in a single time formalism in the case when the phase space is reduced by a set of first class kinematic constraints and the Hamiltonian is introduced as an independent dynamic constraint. For this case in the centre of mass frame the Hamiltonian constraint leads to a time-independent Schroedinger equation which is separable as two independent harmonic oscillators as a special case. (author)