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High Quality Content by WIKIPEDIA articles! In quantum gauge theories, in the Hamiltonian formulation, the wave function is a functional of the gauge connection. A and matter fields, phi. Being a quantum gauge theory, we have to impose first class constraints in the form of functional differential equations. Basically, the Gauss constraint. In flat spacetime, space is noncompact R3. Since the Gauss constraints are local, it suffices to consider gauge transformations U which approach 1 at spatial infinity. Alternatively, we can assume space is a very large three sphere S3 or that space is a compact 3-ball B3 with a S2 boundary where the values of the fields are fixed so that the gauge transformations occur only in the interior of the ball.

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