On the description of unstable particles in quantum field theory
10.1007/bf02727534
Crossref journal-article
Springer Science and Business Media LLC
Il Nuovo Cimento (297)
Bibliography

Lévy, M. (1959). On the description of unstable particles in quantum field theory. Il Nuovo Cimento, 13(1), 115–143.

Authors 1
  1. M. Lévy (first)
References 25 Referenced 117
  1. V. Glaser andG. Källén:Nucl. Phys.,2, 706 (1956). (10.1016/0029-5582(56)90116-X) / Nucl. Phys. by V. Glaser (1956)
  2. P. T. Matthews andA. Salam:Phys. Rev.,112, 283 (1958). See also the discussion inProc. of the Ann. Int. Conf. on High Energy Phys. at CERN (1958), p. 141. (10.1103/PhysRev.112.283) / Phys. Rev. by P. T. Matthews (1958)
  3. H. Araki, Y. Munakata, M. Kawaguchi andT. Gotô:Progr. Theor. Phys.,17, 419 (1957). (10.1143/PTP.17.419) / Progr. Theor. Phys. by H. Araki (1957)
  4. G. Höhler:Zeits. f. Phys.,152, 546 (1958) where the reader will also find more complete references to the literature on the subject. (10.1007/BF01375212) / Zeits. f. Phys. by G. Höhler (1958)
  5. V. Weisskopf andE. Wigner:Zeits. f. Phys.,63, 54 (1930);65, 18 (1930). (10.1007/BF01336768) / Zeits. f. Phys. by V. Weisskopf (1930)
  6. For a summary, seeW. Heitler:Quantum Theory of Radiation, 2nd ed. (Oxford, 1954).
  7. We refer to the work ofK. Nishijima:Phys. Rev.,111, 995 (1958) andW. Zimmermann:Nuovo Cimento,10, 297 (1958), who have shown that fields representing bound states can be constructed, which obey the usual axioms of local field theory. (10.1103/PhysRev.111.995) / Phys. Rev. by K. Nishijima (1958)
  8. R. E. Peierls:Proc. of the 1954 Glasgow Conf. (London, 1955), p. 296.
  9. See some of the references given in Höhler’s paper (4). (10.1007/BF01375212) / Zeits. f. Phys. by G. Höhler (1958)
  10. The propagator’s method seems also more practical than the method proposed byMatthews andSalam (2) who define the mass and life-time of an unstable particle by the first and second moments of a certain mass distribution ϱ(K 2). In many instances, these moments, and especially the second, do not exist, if ϱ(K 2) does not decrease very rapidly for largeK 2. An example is given in Sect.3 (see footnote (17)). (10.1103/PhysRev.112.283) / Phys. Rev. by P. T. Matthews (1958)
  11. T. D. Lee:Phys. Rev.,95, 1329 (1954). (10.1103/PhysRev.95.1329) / Phys. Rev. by T. D. Lee (1954)
  12. G. Källén andW. Pauli:Dan. Mat. Fys. Medd.,30, no. 7 (1955).
  13. When most of this work was done (especially Sects.2 and3), the author had not yet seen the papers quoted in footnotes (3) and (4), who consider, among other things, the complex pole in the propagator of the Lee model. We feel that there is not much duplication with the present paper, where we are more interested in conditions for the analytical continuation to the pole, rather than in its precise location. Höhler’s paper is more concerned with the construction of the time-graph of an unstable particle, and will be discussed in our forthcoming note on this problem. (10.1143/PTP.17.419) / Progr. Theor. Phys. by H. Araki (1957)
  14. We are indebted to Prof.Lehmann for an illuminating discussion on this point.
  15. S. Mandelstam:Phys. Rev.,112, 1344 (1958). (10.1103/PhysRev.112.1344) / Phys. Rev. by S. Mandelstam (1958)
  16. H. Lehmann:Nuovo Cimento,11, 342 (1954). (10.1007/BF02783624) / Nuovo Cimento by H. Lehmann (1954)
  17. Eq. (3.4) provides an example of a mass density, the first and second moments of which may not exist (see footnote (10)). In order to prevent the existence of ghost states, it is sufficient thatΓ(ω) tends to a constant forω → ∞ (this corresponds tof(ω) ∼ω −1/2 for largeω). On the other hand, for the mass and life-time to be defined by the prescription of Matthews and Salam,Γ(ω) must behave likeω −2 for largeω; this corresponds tof(ω) ⋍ω −3/2 and is, of course, much more restrictive. In a relativistic theory, this would imply that the vertexoperator Γ(p 1,p 2) behaves likeW −3, whereW 2=−(p 1+p 2)2. (10.1103/PhysRev.112.283) / Phys. Rev. by P. T. Matthews (1958)
  18. See, for example,S. Bochner andK. Chandrasekharan:Fourier Transforms (Princeton, 1949);G. Doetsch:Theorie und Anwendung der Laplacetransformation (Berlin, 1937).
  19. In the Lee model, there is a simple connection between the propagator and the amplitude:b(t)=<Iv,0,0> exp [−iHt]<Iv,0,0>, the square of which is the probability to «observe» the state |1v, 0, 0| at timet, if |1v, 0, 0| were the only state present att=0. This connection is: $$\frac{1}{2}S'_v (t) = \frac{{b(t)}}{{N^2 }}$$ In the framework of the usual treatment of decaying states, |b(t)|2 would be considered as the time-graph of the V-particle, although we know very well that free states like |l v, 0, 0| do not have much meaning in this case. Consequently, the discussion on the asymptotic behaviour ofS v ′ (t) can be applied also immediately to |b(t|2) (see, for example, ref. (4)). (10.1007/BF01375212) / Zeits. f. Phys. by G. Höhler (1958)
  20. The coefficient of the exponential in |b(t)|2 becomes also equal to unity (see footnote (19)). (10.1007/BF01375212) / Zeits. f. Phys. by G. Höhler (1958)
  21. K. Nakanishi:Progr. Theor. Phys.,19, 607 (1958). (10.1143/PTP.19.607) / Progr. Theor. Phys. by K. Nakanishi (1958)
  22. References to the work on the vertex function are given in the report ofM. L. Goldberger:Proc. of the Ann. Int. Conf. on High Energy Physics at CERN (1958), p. 207; see alsoW. Gilbert: to be published.
  23. For example:M. L. Goldberger andS. B. Treiman:Phys. Rev.,111, 354 (1958);P. Federbush, M. L. Goldberger andS. B. Treiman:Phys. Rev.,112, 642 (1958);M. L. Goldberger andS. B. Treiman:Neutral Pion Decay (preprint). (10.1103/PhysRev.111.354) / Phys. Rev. by M. L. Goldberger (1958)
  24. See,e.g.:S. T. Ma:Rev. Mod. Phys.,25, 853 (1953). (10.1103/RevModPhys.25.853) / Rev. Mod. Phys. by S. T. Ma (1953)
  25. R. Jost:Helv. Phys. Acta,20, 256 (1947). / Helv. Phys. Acta by R. Jost (1947)
Dates
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Created 17 years, 8 months ago (Dec. 18, 2007, 4:37 a.m.)
Deposited 6 years, 3 months ago (May 18, 2019, 6:19 p.m.)
Indexed 2 months, 2 weeks ago (June 8, 2025, 8:29 p.m.)
Issued 66 years, 1 month ago (July 1, 1959)
Published 66 years, 1 month ago (July 1, 1959)
Published Print 66 years, 1 month ago (July 1, 1959)
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@article{L_vy_1959, title={On the description of unstable particles in quantum field theory}, volume={13}, ISSN={1827-6121}, url={http://dx.doi.org/10.1007/bf02727534}, DOI={10.1007/bf02727534}, number={1}, journal={Il Nuovo Cimento}, publisher={Springer Science and Business Media LLC}, author={Lévy, M.}, year={1959}, month=jul, pages={115–143} }