Acausality in the Harish-Chandra equations for composite particles with spins1/2and3/2

Cox, W

doi:10.1088/0305-4470/10/8/019

Cited by 4 publications

(5 citation statements)

References 23 publications

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“…The fact that the multiparticle equations with diagonalizable (3-matrices have no acausal defects in minimal electromagnetic coupling leads to different interpretations. One of the spread interpretations is the following: the high-spin particles are not elementary but the composite ones (see, for example, [ 10 ]). This interpretation is based on the ideas of gauge theories, where the elementary constituents of matter are leptons and quarks.…”

Section: Discussionmentioning

confidence: 99%

“…2) 3d 2 =2a |3°(|3°2 -1) =O. (10) It follows from ( 8) and (10) that in the case of causal propagation ( 3d 2 =2a ), (3°i s diagonalizable. This, in turn, is in accordance with the result of V. Amar and U. Dozzio [ 4 ] that the equations with diagonalizable (3°m atrix are causal in the presence of external electromagnetic field.…”

Section: The Bhabha-gupta Equationmentioning

confidence: 99%

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On the Acausality of Spin 3/2 Wave Equations

Loide¹

1983

Proceedings of the Academy of Sciences of the Estonian SSR. Phy

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Section: Discussionmentioning

confidence: 99%

Section: The Bhabha-gupta Equationmentioning

confidence: 99%

On the Acausality of Spin 3/2 Wave Equations

Loide¹

1983

Proceedings of the Academy of Sciences of the Estonian SSR. Phy

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“…This unpleasant and puzzling phenomenon has generated a vast literature (see Allcock and Hall 1977, Cox 1976 for references).…”

Section: Introductionmentioning

confidence: 99%

“…Such derivatives, if non-zero, are always likely to be dangerous, since they can be made as big as we please by changing the reference frame. Obviously a safe way to avoid acausality troubles would be to use equations free of secondary constraints (Amar and Dozzio 1975, Cox 1976, Prabhakaran er a1 1977. There is however a group-representation theorem of Gel'Fand and Yaglom which, in combination with other established results, completely blocks this escape route.…”

Section: Introductionmentioning

confidence: 99%

“…This is a strong result, since it does not depend upon any of the customary assumptions as to Klein-Gordon conditions, etc. It is probable that it could be still further strengthened, since in practice it is found necessary to bring in quaternary constraints for spin z, sexenary constraints for spin $, and so forth (Amar and Dozzio 1972a, b, Singh and Hagen 1974, Giesen 1975, Cox 1978.…”

Section: Introductionmentioning

confidence: 99%

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Hole-Burnings Observed at High Energy Tails in Spontaneous Emission Spectra from 1.3 µm-InGaAsP/InP Lasers

Yamanishi¹,

Suemune²,

Nonomura³

et al. 1982

Jpn. J. Appl. Phys.

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We trace the failure of Einstein causality in interacting high-spin field theories to the presence of secondary constraints in the Cauchy initial-value problem. We bring in and extend a theorem of Gel'Fand and Yaglom, and use it to show that non-negativity of the field anticommutators for half-integral spin, and non-negativity of the field energy for integral spin, necessarily imply the existence of such constraints, except for the privileged spin values 0, 4 and 1. We prove this under very lax assumptions as to the nature of the mass spectrum.We carry out a systematic search for alternative spin-; constraint schemes, taking a Lagrangian which contains thirteen adjustable parameters, many of which couple in the hitherto 'obscure' unmixed-spinor representations (a, 0) and (O,$ of the Lorentz group.The search reveals two unfamiliar spin-; equations, one of which is entirely new. We analyse the new equations and find that each contains a Rarita-Schwinger constraint subchain. This means that the new equations will also show causality failures.We find that in five or more space-time dimensions additional field equations appear, which are very much simpler and give a much more fundamental role to the 'obscure' representations. We infer that our inability to find a viable alternative to the Rarita-Schwinger scheme reflects an essential mathematical feature of four-dimensional spacetime, and that it is not due just to a lack of imagination. We examine the dimension dependence of the compound-spin equation of Harish-Chandra, and find further support for this assessment. We conclude that the only acceptable dynamical equations in fourdimensional Minkowski space-time are those customarily associated with spins 0, + and 1.

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Constraints, positivity, 'obscure' representations and the spin-3/2 problem

Allcock

Hall

1978

J. Phys. A: Math. Gen.

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Acausality in the Harish-Chandra equations for composite particles with spins¹/₂and³/₂

Cited by 4 publications

References 23 publications

On the Acausality of Spin 3/2 Wave Equations

On the Acausality of Spin 3/2 Wave Equations

Hole-Burnings Observed at High Energy Tails in Spontaneous Emission Spectra from 1.3 µm-InGaAsP/InP Lasers

Constraints, positivity, 'obscure' representations and the spin-3/2 problem

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