Abstract
The conventional formulation of classical relativistic Hamiltonian constraint dynamics ofN interacting particles assumesN constraints which are required to satisfy an Abelian Poisson-bracket algebra. This requirement imposes restrictions on the permitted interactions, resulting in many-body forces. These are difficult to compute for given two-body forces. We propose a perturbative method for this purpose, which is symmetric in the particles. It requires Poincare-invariant integration, which is discussed in detail. An example is solved explicitly.
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