Advertisement

Il Nuovo Cimento B (1971-1996)

, Volume 46, Issue 1, pp 1–15 | Cite as

Conformal relativity, a theory of mass. I: Survey of Theoretical Results

  • R. L. Ingraham
Article

Summary

In a series of papers it will be explained how a kinematic theory of mass follows from adopting the conformal groupC as basic space-time symmetry group. As an aspect of the group, kinematic masses are bare masses; physical masses are to be calculated from these and interactions. The particle solutions are of two kinds: massless, or massive families consisting of theC plus an infinite set of discrete excited mass states. An unexpected consequence of conformal symmetry is the extrapolation of the space-time origin of (some at least) internal symmetries. In particular,C provide isospin labels and the free Lagrangians, pure conformal group constructs, possess isospinSU2 invariance as an accidental («dynamical») symmetry. New possibilities for gauge theories of interactions are also implied. The new way of handling mass allows gauge bosons of nonzero bare mass (as well as massless ones) without violating gauge invariance. Thus Higgs fields and vacuum broken symmetries are no longer necessary in gauge theory.

Конформная теория относительности. Теория массы I: Обэор теоретических результатов

Резюме

В серии работ будет показано, как кинематическая теория масс следует из предпожения, что конформная группаC является основной группой симметрии пространства-времени. Кинематические массы представляют затравочные массы; физические массы вычисляются с помощью кинематических масс и взаимодействий. Частичные решения оказываются двух типов: с нулевой массой илн массивные семейства, состоящие изC-мультиплета плюс бесконечная система дискретных возбужденных состояний. Неожиданное следствие конформной симметрии представляет общяснение пространственно-временного происхождения внутренних симметрий. В частности,C-мультиплеты обеспечивают классификацию изоспина, а свободные Лагранжианы обладают изоспиновойSU2 инвариантностью как случайной («динамической») симметрией. Из рассмотрения вытекают новые возможности для калибровочных теорий взаимодействий. Предложенный подход допускает калибровочные бозоны с ненулевой затравочной массой, без нарушения калибровочной инвариантости. Таким образом, в калибровочной теории поля Хиггса и нарушенные симметрии вакуума не являются более необходимыми.

Riassunto

In una serie di lavori di spiega come dall'adottare il gruppo conformeC come gruppo di simmetria basilare per lo spazio-tempo derivi una teoria cinematica della massa. Come uno degli aspetti del gruppo, le masse cinematiche sono masse nude; le masse fisiche devono essere calcolate da queste e dalle interazioni. Le soluzioni per le particelle sono di due tipi: senza massa, o famiglie massive che consistono del multiplettoC più una serie infinita di stati eccitati discreti di massa. Una conseguenza inattesa della simmetria conforme è l'estrapolazione dell'origine spazio-temporale di (almeno alcune) simmetrie interne. In particolare, i multiplettiC forniscono segnature di isospin e le lagrangiane libere, semplici strutture di gruppo conformi, possiedono invarianza di isospinSU2 come simmetria («dinamica») casuale. Si intuiscono anche nuove possibilità di teorie di gauge. Il nuovo modo di trattare la massa permette bosoni di gauge con massa semplice diversa da zero (e anche quelli senza massa) senza violare l'invarianza di gauge. Così i campidi Higgs e le simmetrie rotte del vuoto non sono più necessari nella teoria di gauge.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    We shall use natural units ħ=c=1. The metric isg μν=diag (+ + + −) 1.Google Scholar
  2. (2).
    This speculation concernsbare («unrenormalized», «undressed») masses. Also we mean observed «particles», whether they be elementary or composite.Google Scholar
  3. (3).
    For example, the gauge theories of unified weak, EM and strong forces in the last ten years.Google Scholar
  4. (4).
    Cf. «The Key to the Universe», a television broadcast co-produced by the BBC and WTTW, Chicago.Google Scholar
  5. (5).
    The credit for this idea and for the first solutions belongs toY. Murai.Google Scholar
  6. (7).
    That isM 5 has more structure than just the Riemannian geometryV 5. Part II will make this clear.Google Scholar
  7. (8).
    Herex μ, μ=1 to 4, withx 4t (notit please!) are the usual Cartesian space-time co-ordinates. The indices μ, ν, λ, ξ, … will be reserved for these co-ordinates. λ is the ‘phere» radius, see part II.p·xp μ x μ=p·xp 4 t. We suppress any amplitudes in eqs (2) and (3a).Google Scholar
  8. (10).
    R. L. 0115 0245 V 3 Ingraham: inLectures in Theoretical Physics (Boulder, Colo., 1969).Google Scholar
  9. (11).
    Needless to say, by «fit» we mean that the quantum numbers fit. The real (renormalized) masses must come out of conformal QFT. There is good reason to believe that there will be qualitative differences with results based on present-day QFT because mass is handled so differently. For example, whenever a virtual massive particle appears in a Feynman graph, that graph must be summed over its entire mass family.Google Scholar
  10. (12).
    C. J. Isham, A. Salam andJ. Strathdee: ICTP 0115 0245 V 3 preprint IC/73/53 (1973).Google Scholar
  11. (14).
    R. L. Ingraham andM. A. Melvin:Nuovo Cimento,29, 1034 (1963). For remarks on the R (right handed) leptons, see below.CrossRefGoogle Scholar
  12. (15).
    C. N. Yang andR. L. Mills:Phys. Rev.,96, 191 (1954).MathSciNetADSCrossRefGoogle Scholar
  13. (16).
    R. Utiyama:Phys. Rev.,101, 1597 (1956).MathSciNetADSCrossRefGoogle Scholar
  14. (17).
    By «ρ-meson» we shell denote the whole massive family with the quantum numbers (T, J)=(1, 1) of the ρ. Again, no final particle interpretation is implied.Google Scholar
  15. (18).
    Boldface means isospace vector.Google Scholar
  16. (19).
    Since the theory predicts both L and R neutrinos, there are two courses open. The most theoretically appealing is to keep the R-neutrino and assign leptonT=1/2 to all leptons, thus implying that the R-neutrino has not yet been seen,e.g., because it is too massive (physical, not bare mass!). This semi-weak Lagrangian would then conserve parity. The other is to exclude the R-neutrino by fiat, assign leptonT=0 to the R-electron, and couple W only to the L-leptons. This would break parity «maximally» in the usual way.Google Scholar
  17. (20).
    Apart from the photon interaction terms of course, which break isospin symmetry in the usual way.Google Scholar
  18. (21).
    SeeJ. Bernstein:Rev. Mod. Phys.,46, 7 (1974) for a readable review of these «spontaneously broken symmetry» theories.ADSCrossRefGoogle Scholar
  19. (22).
    In Weinberg's 1967 theory (see ref. (21) one starts with massless gauge bosonsa andb mediating local lepton hypercharge and isospin groups and then gets the photon as a linear combination ofa andb 3. Consequently his semi-weak interaction Lagrangian is notSU 2 invariant, nor is the effective current-current leptonic weak interaction obtained from it by exchanging virtual W+, W and Z0 in second order. On the other hand, our semi-weak interaction isSU 2 invariant, and so is the effectivejj leptonic weak interaction. These two cases could be distinguished experimentally by selection rules in processes involving neutral currents. Also note that Weinberget al.'s interesting scheme could not be used here. For, since we would want to take at least theb fields as massive, there would be no hope of getting a massless photon.ADSCrossRefGoogle Scholar
  20. (24).
    We anticipate that, in the event thatSU 3 symmetry is discovered in a more complete Lagrangian, eqs. (7) and (8) will be the model of how the whole pseudoscalar octet is introduced along with the whole vector-meson octet.Google Scholar
  21. (25).
    The significance, if any, of this is not understood. But, if all of this could be extended to localSU 3 (cf. ref. (24)) for leptons as well as baryons, it might have something to do with the Cabibbo rotation.Google Scholar
  22. (26).
    R. L. Ingraham:Nuovo Cimento,9, 886 (1952). Much of this paper should be ignored as outdated by later work.MathSciNetCrossRefGoogle Scholar
  23. (27).
    Since these are the excited, «primed» states of the Rosenfeld tables, we doubt that there are any experimental data on this.Google Scholar
  24. (28).
    See, for example,R. Adler, M. Bazin andM. Schiffer:Introduction to General Relativity, 2nd ed., Chap. 9 (New York, N. Y., 1975).Google Scholar

Copyright information

© Società Italiana di Fisica 1978

Authors and Affiliations

  • R. L. Ingraham
    • 1
  1. 1.Research CenterNew Mexico State UniversityLas Cruces

Personalised recommendations