Hadamard states via fermionic projectors in a time-dependent external potential

New Trends in Algebraic Quantum Field Theory (AQFT2015)
Simone Murro on February 13, 2015
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We give a non-perturbative construction of the fermionic projector in Minkowski spacetime coupled to a time-dependent external potential which is smooth and decays faster than quadratically for large times. The weak and strong mass oscillation properties are proven. We show that the integral kernel of the fermionic projector is of Hadamard form, provided that the time integral of the spatial sup-norm of the potential satisfies a suitable bound. This gives rise to an algebraic quantum field theory of Dirac fields in an external potential with a distinguished, pure, quasi-free Hadamard state.

Related papers:
The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States