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Spin-foam models are hoped to provide a dynamics for loop quantum gravity.These start from the Plebanski formulation of gravity, in which gravity isobtained from a topological field theory, BF theory, through constraints,which, however, select more than one gravitational sector, as well as anunphysical degenerate sector. We show this is why terms beyond the neededFeynman-prescribed one appear in the semiclassical limit of the EPRL spin-foamamplitude. By quantum mechanically isolating a single gravitational sector, wemodify this amplitude, yielding a spin-foam amplitude for loop quantum gravitywith the correct semiclassical limit.

A spin-foam vertex amplitude with the correct semiclassical limit