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Computing dynamical properties of strongly interacting quantum many-bodysystems poses a major challenge to theoretical approaches. Usually, one has toresort to numerical analytic continuation of results on imaginary frequencies,which is a mathematically ill-defined procedure. Here, we present an efficientmethod to compute the spectral functions of the two-component Fermi gas nearthe strongly interacting unitary limit directly in real frequencies. To thisend, we combine the Keldysh path integral that is defined in real time with theself-consistent T-matrix approximation. The latter is known to predictthermodynamic and transport properties in good agreement with experimentalobservations in ultracold atoms. We validate our method by comparison withthermodynamic quantities obtained from imaginary time calculations and bytransforming our real-time propagators to imaginary time. By comparison withstate-of-the-art numerical analytic continuation of the imaginary time results,we show that our real-time results give qualitative improvements for dynamicalquantities. Moreover, we show that no significant pseudogap regime exists inthe self-consistent T-matrix approximation above the critical temperature$T_c$, an issue that has been under significant debate. We close by pointingout the versatile nature of our method as it can be extended to other systems,like the spin- or mass-imbalanced Fermi gas, other Bose-Fermi models, 2Dsystems as well as systems out of equilibrium.

Spectral functions of the strongly interacting 3D Fermi gas