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The nonlocal correlation mechanism between excitonic pairs is considered fora two dimensional exciton system. On the base of the unitary decomposition ofthe usual electron operator, we include the electron phase degrees of freedominto the problem of interacting excitons. Applying the path integral formalism,we treat the excitonic insulator state (EI) and the Bose-Einstein condensation(BEC) of preformed excitonic pairs as two independent problems. For the BEC ofexcitons the phase field variables play a crucial role. We derive theexpression of the local EI order parameter by integrating out the phasevariables. Then, considering the zero temperature limit, we obtain theexcitonic BEC transition probability function, by integrating out the fermions.We calculate the normal excitonic Green functions for the conduction andvalence band electrons and we derive the excitonic spectral functions, bothanalytically and numerically. Different values of the Coulomb interactionparameter are considered.

Phase coherence and spectral functions in the two-dimensional excitonic systems