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Evolutionary Laws, Initial Conditions, and Gauge Fixing in Constrained Systems
We describe in detail how to eliminate nonphysical degrees of freedom in the
Lagrangian and Hamiltonian formulations of a constrained system. Two important
and distinct steps in our method are the fixing of ambiguities in the dynamics
and the determination of inequivalent initial data. The Lagrangian discussion
is novel, and a proof is given that the final number of degrees of freedom in
the two formulations agrees. We give applications to reparameterization
invariant theories, where we prove that one of the constraints must be
explicitly time dependent. We illustrate our procedure with the examples of
trajectories in spacetime and with spatially homogeneous cosmological models.
Finally, we comment briefly on Dirac's extended Hamiltonian technique.Comment: 23 pages; plain TeX. To appear: Classical & Quantum Gravit
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