We give a non-perturbative construction of the fermionic projector in Minkowski space 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 the 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.

The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states

Murro S.;
2016

Abstract

We give a non-perturbative construction of the fermionic projector in Minkowski space 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 the 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/1069922
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