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We study expectation values of observables in three-dimensional spinfoamquantum gravity coupled to Dirac fermions. We revisit the model introduced byone of the authors and extend it to the case of massless fermionic fields. Weintroduce observables, analyse their symmetries and the corresponding propergauge fixing. The Berezin integral over the fermionic fields is performed andthe fermionic observables are expanded in open paths and closed loopsassociated to pure quantum gravity observables. We obtain the vertex amplitudesfor gauge-invariant observables, while the expectation values of gauge-variantobservables, such as the fermion propagator, are given by the evaluation ofparticular spin networks.

Observables in 3d spinfoam quantum gravity with fermions