Off-shell self-energy for 1-D Fermi liquids

The self-energy in Born approximation including exchange of interacting one-dimensional systems is expressed in terms of a single integral about the potential which allows a fast and precise calculation for any potential analytically. The imaginary part of the self-energy as damping of single-particle excitations shows a rich structure of different areas limited by single-particle and collective excitation lines. The corresponding spectral function reveals a pseudogap, a splitting of excitations into holons and antiholons as well as bound states.