Concept

Hamiltonian constraint

Résumé
The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint of general relativity is an important non-trivial example. In the context of general relativity, the Hamiltonian constraint technically refers to a linear combination of spatial and time diffeomorphism constraints reflecting the reparametrizability of the theory under both spatial as well as time coordinates. However, most of the time the term Hamiltonian constraint is reserved for the constraint that generates time diffeomorphisms. Simplest example: the parametrized clock and pendulum system Parametrization In its usual presentation, classical mechanics appears to give time a special role as an independent variable. This is unnecessary, however. Mechanics can be formulated to treat the time variable on the same footing as the other variables in an extended phase space, by parameterizing the temporal variable(
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