Summary
For elastic scattering of particles of arbitrary spin, an invariant amplitude is constructed which has the «positivity» required for Martin's proof of Froissart bounds.
Riassunto
Per lo scattering elastico di particelle di spin arbitrario, si costruisce un'ampiezza invariante che ha la «positività» richiesta per la prova di Martin dei vincoli di Froissart.
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References
G. Mahoux andA. Martin:Phys. Rev.,174, 2140 (1968).
A. Martin:Nuovo Cimento,42 A, 930 (1966).
See for example,G. Cohen-Tannoudji, A. Morel andH. Navelet:Ann. of Phys.,46, 111 (1968) and references therein.
K. Yamamoto:Nuovo Cimento,27, 1277 (1963).
A. Martin:Phys. Rev.,129, 1432 (1963).
J. Bros, H. Epstein andV. Glaser:Nuovo Cimento,31 1265 (1964).
See ref. (1). or note that the property holds form=0 and that the reduction formula d cos nθ/d cosθ = n sin nθ/sinθ = (n sin (n-2)θ)/sinθ+2 cos (n-1)θ allows the first derivative, and then any derivative, to be expressed as a superposition of terms cosn′θ with positive coefficients.
V. Bargmann andE. Wigner:Proc. Natl. Acad. Sci., Wash.,34, 211 (1948). For the relation of these amplitudes to others see the Appendix.
M. Jacob andG. C. Wick:Ann. of Phys.,26, 322 (1964).
H. P. Stapp:Phys. Rev.,125, 2139 (1962).
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Bell, J.S. Froissart bounds with any spin. Nuovo Cimento A (1965-1970) 61, 541–552 (1969). https://doi.org/10.1007/BF02756861
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DOI: https://doi.org/10.1007/BF02756861