Here the weak equality means that the Poisson bracket could result in terms proportional one of the constraints, the classical Poisson brackets for the relativistic two-body system being defined by { O 1 , O 2 } = ∂ ∂ O 1 ∂ ∂ x 1 μ μ ∂ ∂ O 2 ∂ ∂ p 1 μ μ − − ∂ ∂ O 1 ∂ ∂ p 1 μ μ ∂ ∂ O 2 ∂ ∂ x 1 μ μ + ∂ ∂ O 1 ∂ ∂ x 2 μ μ ∂ ∂ O 2 ∂ ∂ p 2 μ μ − − ∂ ∂ O 1 ∂ ∂ p 2 μ μ ∂ ∂ O 2 ∂ ∂ x 2 μ μ .