Causal localizations in relativistic quantum mechanics

Castrigiano, Domenico P. L.; Leiseifer, Andreas D.

doi:10.1063/1.4923196

Cited by 7 publications

(14 citation statements)

References 50 publications

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“…Derivations of the Dirac equation from first physics principles, in both flat and curved 4D space-times were previously discussed [22,[24][25][26][27]. Still, the Dirac equation has been criticized for the Klein paradox [28][29][30][31] and causality violation [32][33][34][35] in quantum mechanics. The Klein paradox may be solved by imposing smooth interaction potentials (i.e., smooth space-time manifold) for the Dirac equation [29].…”

Section: On 5d Space-time and 5d Null Propagationmentioning

confidence: 99%

The 4D Dirac Equation in Five Dimensions

Breban

2018

Annalen der Physik

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The Dirac equation may be thought as originating from a theory of five-dimensional (5D) spacetime. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time manifold. We explain how the 5D null formalism breaks down to four dimensions to recover two single-particle theories. Namely, we obtain Dirac's relativistic quantum mechanics and a formulation of statistical mechanics. Exploring the non-relativistic limit in five and four dimensions, we identify a new spin-electric interaction with possible applications to magnetic resonance spectroscopy (within quantum mechanics) and superconductivity (within statistical mechanics).

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Section: On 5d Space-time and 5d Null Propagationmentioning

confidence: 99%

The 4D Dirac Equation in Five Dimensions

Breban

2018

Annalen der Physik

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“…If now the apparatus A is boosted by a Lorentz transformation L given by A ∈ SL(2, C) then, again by relativistic symmetry, the boosted apparatus realizes the observable W (A)E(∆)W (A) −1 . Moreover, by special relativity, the boosted apparatus is still suited for position measurement, namely in the spatial region L ∆ of the spacelike hyperplane L R 3 in Minkowski space R 4 . Here, for convenience, R 3 is identified with {0} × R 3 .…”

Section: 1mentioning

confidence: 99%

“…Partially we follow Thaller 1992 [26, Theorem 1.6] minimizing the assumptions. 4 Lemma ( 5) is a version of Hegerfeldt, Ruijsenaars 1980 [18,II]. Let S be a representation of the group R 3 of spatial translations.…”

Section: Positive Energy and Localized Statesmentioning

confidence: 99%

“…For further references see [6] 2017. Also more recently, in [4] 2015 a thorough investigation of causal time evolution for massive relativistic quantum systems is presented, to which we will refer recurrently. Some indicated parts of it are simply taken over for the sake of completeness.…”

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confidence: 99%

“…For massive systems the steps (a) and (b) are done in [4] yielding a complete and explicit description of the SCT reported in sec. 22.1.…”

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confidence: 99%

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Dirac and Weyl Fermions -- the Only Causal Systems

Castrigiano

2017

Preprint

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Causal systems describe the localizability of relativistic quantum systems complying with the principles of special relativity and elementary causality. At their classification we restrict ourselves to real mass and finite spinor systems. It follows that (up to certain not yet discarded unitarily related systems) the only irreducible causal systems are the Dirac and the Weyl fermions. Their wave-equations are established as a mere consequence of causal localization. -The compact localized Dirac and Weyl wave-functions are studied in detail. One finds that, at the speed of light, the carriers shrink in the past and expand in the future. For every direction in space there is a definite time at which the change from shrinking to expanding occurs. A late changing time characterizes those states, which shrink to a δ-strip if boosted in the opposite direction. Using a density result for these late-change states one shows that all Dirac and Weyl wave-functions are subjected to Lorentz contraction. -We tackle the question whether a causal system induces a representation of a causal logic and thus provides a localization in proper space-time regions rather than on spacelike hyperplanes. The causal logic generated by the spacelike relation is shown to do not admit representations at all. But the logic generated by the non-timelike relation in general does, and the necessary condition is derived that there is a projection valued measure on every non-timelike non-spacelike hyperplane being the high boost limit of the localization on the spacelike hyperplanes. Dirac and Weyl systems are shown to satisfy this condition and thus to extend to all non-timelike hyperplanes, which implies more profound properties of the causal systems. The compact localized eigenstates of the projections to non-spacelike flat strips are latechange states.

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Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt’s Theorem

Finster

Paganini

2022

Ann. Henri Poincaré

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We prove quantitative versions of the following statement: If a solution of the $$1+1$$ 1 + 1 -dimensional wave equation has spatially compact support and consists mainly of positive frequencies, then it must have a significant high-frequency component. Similar results are proven for the $$3+1$$ 3 + 1 -dimensional wave equation.

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Causal localizations in relativistic quantum mechanics

Cited by 7 publications

References 50 publications

The 4D Dirac Equation in Five Dimensions

The 4D Dirac Equation in Five Dimensions

Dirac and Weyl Fermions -- the Only Causal Systems

Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt’s Theorem

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