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We revise imposition of various constraints in spin foam models of4-dimensional general relativity. We argue that the usual simplicity constraintmust be supplemented by a constraint on holonomies and together they must beinserted explicitly into the discretized path integral. At the same time, theclosure constraint must be relaxed so that the new constraint expressescovariance of intertwiners assigned to tetrahedra by spin foam quantization. Asa result, the spin foam boundary states are shown to be realized in terms ofprojected spin networks of the covariant loop approach to quantum gravity.

Simplicity and closure constraints in spin foam models of gravity