Quantization of Dirac fields in static spacetime

On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for advanced and retarded fundamental solutions and for the propagator. Finally, we use a fermion Fock space based on the positive/negative energy split to define a Dirac quantum field operator whose commutator is the propagator.Comment: LaTex2e, 17 page

Unveiling a hidden fortification system at “Faraglioni” Middle Bronze Age Village of Ustica Island (Palermo, Italy) through ERT and GPR prospections

We carried out a geophysical research project in the Middle Bronze Age village of Ustica (Palermo, Sicily, Italy), named “Faraglioni Village” after the stack formations which detach from the coast north of the archaeological site. The investigation, which comprised Electrical Resistivity Tomography (ERT) and Ground Penetrating Radar (GPR) techniques, allowed us to discover the buried foundations of an outwork fortification system never evidenced by previous archaeological studies, only hypothesised from the observation of aerial photography and partially outcropping boulders, which align roughly parallel to the main defensive wall of the Village. Our geophysical prospection involved the entire 250 m-long arc of the outward village defensive wall, with the acquisition of eleven ERT profiles and 27 GPR scans. The techniques were selected based on both favourable logistics and methods applicability: ERT sections allowed us to trace a series of high-resistivity anomalies arranged to form an arc-shaped structure along the perimeter of the defensive wall. GPR investigation was localised in the most accommodating patch of terrain of the site, with the effort of intercepting clear enough sections of the target, to determine more accurately its shape, depth, and overall dimensions. Our discovery paves the way for new investigations, mainly aimed at defining the timing of construction of the fortification system, as well as the function of the remains of other architectural structures identified close to the wall, which could represent the target of further geophysical investigations