  We calculate non-perturbative self-consistent fermionic and bosonic spectral
functions of ultra-cold Fermi gases with the spectral functional approach. This
approach allows for a direct real-time computation of non-perturbative
correlation functions, and in the present work we use spectral Dyson-Schwinger
equations. We focus on the normal phase of the spin-balanced Fermi gas and
provide numerical results for the full fermionic and bosonic spectral
functions. The spectral functions are then used for the determination of the
equation of state, the Tan contact and ejection rf spectra at unitarity. These
results are compared to experimental data, the self-consistent T-matrix
approach and lattice results. Our approach offers a wide range of applications,
including the ab initio calculation of transport and spectral properties of the
superfluid phase in the BCS-BEC crossover.
