Constraint formalism of classical mechanics

Abstract

The constraint formalism for classical mechanics is developed with an eye toward facilitating a manifestly covariant relativistic quantization of classical mechanics. The very close relationship of this formalism to the more familiar Hamiltonian formalism has long obscured its independent status. In this paper, after defining the concept of a classical trajectory in a particularly natural and intrinsic way (that is, without reference to a special parameter such as the time), we prove that the trajectories satisfy the Hamilton equations of motion. In the following paper, the power of this formalism is demonstrated, when as an illustrative example it is employed to solve the nontrivial relativistic two-body problem, both classically and quantum mechanically.