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Reference.org
Diffeomorphism constraint
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<p>In <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>, it is often important to study theories with the <a href="/facts/Diffeomorphism/855N5YYj">diffeomorphism</a> <a href="/facts/Symmetry/hpu7DK8p">symmetry</a> such as <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>. These theories are invariant under arbitrary coordinate transformations. Equations of motion are generally derived from the requirement that the <a href="/facts/Group_action_(mathematics)/Vh9VtUUw">action</a> is stationary. There are special variations that are equivalent to spatial diffeomorphisms. The invariance of the action under these variations implies non-dynamical equations of motion i.e. constraints. These equations must be satisfied or, at least, they must annihilate the physical states in a quantum version of the theory. </p>