A new class of Fermionic Projectors: Møller operators and mass oscillation properties
Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in Finster and Reintjes (Adv Theor Math Phys 20:1007, 2016). This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built.
KeywordsDirac fields Fermionic Projector Mass oscillation property Møller operator Quasi-free states Self-dual CAR algebra
Mathematics Subject Classification81T05 81T20 81Q10 46N50
We would like to thank Claudio Dappiaggi, Felix Finster, Christian Gérard, Valter Moretti and Nicola Pinamonti for helpful discussions and comments on the manuscript. We are grateful to the referee for useful comments on the manuscript. S.M. is supported within the DFG research training group GRK 1692 “Curvature, Cycles, and Cohomology” and he is grateful to the department of mathematics of the University of Genoa for the kind hospitality during part of the realization of this work. N.D. is supported by a Ph.D. grant of the university of Genoa, and he is grateful to the department of mathematics of the Université de Paris-Sud for the kind hospitality during part of the realization of this work. The work for this paper was partly carried out during the program Modern Theory of Wave Equations at the Erwin Schrödinger Institute, and we are grateful to the ESI for support and the hospitality during our stay.
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