I rigorously analyze a proposal, introduced by D.R.Terno, about a spatial localization observable for a Klein-Gordon massive real particle in terms of a Poincar´ecovariant family of POVMs. I prove that these POVMs are actually a kinematic deformation of the Newton-Wigner PVMs. The first moment of one of these POVMs however exactly coincides with a restriction (on a core) of the Newton-Wigner selfadjoint position operator, though the second moment does not. This fact permits to preserve all nice properties of the Newton-Wigner position observable, dropping the unphysical features arising from the Hegerfeldt theorem. The considered POVM does not permit spatially sharply localized states, but it admits families of almost localized states with arbitrary precision. Next, I establish that the Terno localization observable satisfies part of a requirement introduced by D.P.L.Castrigiano about causal temporal evolution concerning the Lebesgue measurable spatial regions of any Minkowskian reference frame. The validity of the complete Castrigiano’s causality requirement is also proved for a notion of spatial localization which generalizes Terno’s one in a natural way.

On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles / Moretti, Valter. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 2023, 113:60(2023), pp. 6601-6650. [10.1007/s11005-023-01689-5]

On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles

Moretti, Valter
2023-01-01

Abstract

I rigorously analyze a proposal, introduced by D.R.Terno, about a spatial localization observable for a Klein-Gordon massive real particle in terms of a Poincar´ecovariant family of POVMs. I prove that these POVMs are actually a kinematic deformation of the Newton-Wigner PVMs. The first moment of one of these POVMs however exactly coincides with a restriction (on a core) of the Newton-Wigner selfadjoint position operator, though the second moment does not. This fact permits to preserve all nice properties of the Newton-Wigner position observable, dropping the unphysical features arising from the Hegerfeldt theorem. The considered POVM does not permit spatially sharply localized states, but it admits families of almost localized states with arbitrary precision. Next, I establish that the Terno localization observable satisfies part of a requirement introduced by D.P.L.Castrigiano about causal temporal evolution concerning the Lebesgue measurable spatial regions of any Minkowskian reference frame. The validity of the complete Castrigiano’s causality requirement is also proved for a notion of spatial localization which generalizes Terno’s one in a natural way.
2023
60
Moretti, Valter
On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles / Moretti, Valter. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 2023, 113:60(2023), pp. 6601-6650. [10.1007/s11005-023-01689-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/379089
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