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<p>80.187.106.161: Mobbing removed</p> <hr /> <div>{{Orphan|date=February 2009}}<br /> {{Unreferenced|date=February 2007}}<br /> <br /> In [[theoretical physics]], a '''constraint algebra''' is a linear space of all [[Constraint (mathematics)|constraint]]s and all of their polynomial functions or functionals whose action on the physical vectors of the [[Hilbert space]] should be equal to zero.<br /> <br /> For example, in electromagnetism, the equation for the [[Gauss' law]]<br /> :&lt;math&gt;\nabla\cdot \vec E = \rho&lt;/math&gt;<br /> is an equation of motion that does not include any time derivatives. This is why it is counted as a constraint, not a dynamical equation of motion. In [[quantum electrodynamics]], one first constructs a Hilbert space in which Gauss' law does not hold automatically. The true Hilbert space of physical states is constructed as a subspace of the original Hilbert space of vectors that satisfy<br /> :&lt;math&gt;(\nabla\cdot \vec E(x) - \rho(x)) |\psi\rangle = 0.&lt;/math&gt;<br /> In more general theories, the constraint algebra may be a [[noncommutative algebra]].<br /> <br /> == See also ==<br /> *[[First class constraints]]<br /> <br /> [[Category:Quantum mechanics]]<br /> [[Category:Quantum field theory]]<br /> <br /> {{phys-stub}}</div>

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