Summary
The free-field equations for the metric bosons, that is the linearized field equations for the conformal metric, are solved and the solutions classified in this paper. The metric bosons comprise symmetric,h αβ, and skew-symmetric,f αβ, 5-tensors, where the latter is a 5-curl:f αβ=∂α f β−∂β f α. As for the fermion case (part III) the solutions fall into two general types: massless, or massive resonance families with discrete bare mass spectra. Solutions which fit the photon, the graviton, the ρ, ω etc. spin-1 mesons, the π, η etc. spin-0 mesons and the spin-2 f-meson are found, among others.
Riassunto
Si risolvono le equazioni di campo libero per bosoni metrici, cioè le equazioni di campo linearizzate per la metrica conforme, e si classificano in questo lavoro le soluzioni. I bosoni metrici comprendono 5-tensori simmetricih αβ e a simmetria obbliquaf αβ, dove gli ultimi sono a 5 curvature:f αβ=∂α f β−∂β f α. Come nel caso dei fermioni (parte III), le soluzioni appartengono a due tipi generali: senza massa, o famiglie di risonanza massive con spettri discreti puri di massa. Si trovano, tra le altre, soluzioni che approssimano il fotone, il gravitone, i mesoni ρ, ω, etc., con spin 1, i mesoni π, η, etc. con spin 0 e il mesone f con spin 2.
Резюме
Решаются уравнения свободного поля для метрических бозонов, представляющие линеаризованные уравнения поля для конформной метрики. Проводится классификация ремений. Метрические бозоны включают в себя симметричные,h αβ, и кососимметричные,f αβ, 5-тензоры, где последний есть 5-ротор:f αβ=∂α f β−∂β f α. Дла фермионного случая решения распадаются на два общих типа: семейства резонансов с нулевой массой или с массой отличной от нуля с дискретными спектрами затравочных масс. Получаются решения, которые соответствуют фотону, гравитону, ρ, ω и т.д. мезонам со спином 1, π, η и т.д. мезонам со спином 0 и f мезону со спином 2.
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References
R. L. Ingraham:Phys. Rev.,101, 1411 (1956).
In general allV 5-tensors transform like Poincaré tensors in indices μ, ν, ... and like Poincaré scalars in indices 5.
It would be desirable to derive a unified expression for all the_ℰ-generators on the second quantized field from the action principle as this was done for the spinor IURs, cf. eq. III (6.22).
In fact, the spin-0 fields cancel entirely out of the full (self-coupled) boson Lagrangian, cf. the remarks after eq. I (7).
SeeR. Adler, M. Bazin andM. Schiffer:Introduction to General Relativity, 2nd edition, Chap.9 (New York, N. Y., 1975), for a good exposition of this Weyl theory.
C μν is of course symmetric; we give only the independent nonzero components.
See ref. (12) SeeR. Adler, M. Bazin andM. Schiffer:Introduction to General Relativity, 2nd edition, Chap.9 (New York, N. Y., 1975), for a good exposition of this Weyl theory, subsect.11 2.
For example, terms likeh μν h μν/5 are present, which lead to nonorthogonality of mass modes.
Remember theh αβ are dimensionless,f α have dimensions (length)−1.
ForC·k=0 by eq. (4.3) for ther=±1 4-vector modes.
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Ingraham, R.L. Conformal relativity. Nuov Cim B 46, 261–286 (1978). https://doi.org/10.1007/BF02728621
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DOI: https://doi.org/10.1007/BF02728621