André Martin (physicist)

André Jean Martin (Paris, 20 September 1929–Geneva, 11 November 2020[1][2]) was a French particle physicist who worked at CNRS and CERN.

Biography

After studying at the École normale supérieure (class of 1949),[3] he began his career as a CNRS researcher under the direction of Maurice Lévy at the physics laboratory of the École Normale. He joined CERN in 1959 as a fellow in the Theory Division and became a permanent theoretical physicist in 1964.

In 1958 he helped found the Institut d'Études Scientifiques de Cargèse (Corsica).[4]

In 1959 he married Alice-Anne Schubert, known as Schu, who died in 2016, and had two sons, Philippe and Thierry.

In 1994, he received the status of Physicist Emeritus, a status which has been renewed to this day. André Martin had scientific contacts all over the world: Europe, Asia, North America. He has made numerous visits to the United States, including two one-year visits to the Institute for Advanced Study at the invitation of J.R. Oppenheimer and to New York University, Stony Brook, at the invitation of C.N. Yang.

Scientific work

The most interesting results of Maurice Lévy's thesis are the reconstruction of a separable interaction from a phase shift[5] and an original demonstration of Levinson's theorem.[6] At CERN he first worked on the analytical properties of the amplitude of scattering by a potential: on the one hand a demonstration of the Mandelstam representation for a Yukawa potential,[7] on the other hand a new method for studying partial waves using the Laplace transform.[8]

After the proof, due to Froissart, that the total effective cross section cannot grow faster than the logarithm squared of the energy, using the Mandelstam representation,[9] he is interested in the amplitude of high-energy scattering. He proves that Froissart's result for fixed-angle scattering can be improved.[10] Finally, in 1966 he succeeded in demonstrating the validity of the Froissart bound using local field theory, without postulating the Mandelstam representation.[11] In the meantime, in 1964, he obtains an absolute bound on the pion-pion scattering amplitude,[12] this bound was considerably improved later.[13]

He also proved the convergence of Padé's approximates for the levels of the anharmonic oscillator.[14] He treated the relativistic effects on the instability of boson stars.[15][16]

In 1977, stimulated by experimental results on quarkonium, formed from a heavy quark and antiquark, he began to study the order of energy levels in potentials, but it was not until 1984 that the best criterion, the Laplacian sign of potential, was found.[17] At the same time, in 1981, he proposed a naïve model of potential to reproduce the levels of quarkonium, whose predictive power is extraordinary.[18] This model was also applied to baryons formed from 3 quarks with great success by Jean Marc Richard.[19] An overview of these results can be found in the book written with H.Grosse[20] and a more recent unpublished review can be found in ArXives.[21]

He invented a geometrical method to study the stability of 3-body charged particle systems.[22][23]

André Martin has also studied low-energy scattering in the case of two dimensions of space[24] as well as the counting of related states.[25]

Recent work (after 2008) includes a lower bound on the inelastic rms cross-section,[26] the sign of the real part of the forward scattering amplitud[27] and a lower bound on the wide-angle scattering amplitude.[28]

Books
  • F. Cheung and A. Martin: Analyticity Properties and Bounds on Scatteirng Amplitudes, Gordon nd Breach 1970
  • A.Martin: Scattering Theory: Unitarity, Analyticity and Crossing, Notes byR Schrader, Springer-Verlag 1969
  • (en) Harald Grosse (de) and A. Martin, Particle Physics and the Schrödinger Equation, Cambridge University Press, 1998 (ISBN 0-521-44425-X, read online [archive]).

Awards

References
  1. "André Martin (1929 – 2020)". CERN. Retrieved 12 January 2021.
  2. "Hommages - Pour que son souvenir demeure: André MARTIN". hommages.ch. Retrieved 20 November 2020.
  3. "L'annuaire | a-Ulm". archicubes.ens.fr. Archived from the original on 20 May 2015. Retrieved 19 December 2019.
  4. Luc Allemand et Vincent Moncorgé, Les jardins de la physique, CNRS éditions, 2017, p. 38
  5. A. Martin et M.Gourdin., « Exact determination of a phenomenogical separable interaction », Nuovo Cimento, 11 (1959), p. 670
  6. A. Martin, « On the validity of the Levinson Theorem for non local interactions », Nuovo Cimento, 7, ( 1958), p. 607
  7. A.Martin, J. Bowcock. A Mandelstam, « Representation for potential scattering », Nuovo Cimento, 14, ( 1959), p. 516
  8. A.Martin, « Analyticity of partial waves obtained from the Schrödinger equation », Nuovo cimento, 14, (1959), p. 516
  9. M.Froissart, « Asymptotic Behavior and Subtractions in the Mandelstam Representation », Phys. Rev, 123, (1961), p. 1053
  10. A.Martine, T.Kinoshita et J.J. Loeffel, « A new upper bound for fixed angle scattering amplitudes », Phys. Letters, 10, (1963), p. 460
  11. A.Martin, « Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity: », Nuovo Cimento, 42, (1966), p. 930
  12. An absolute bound on the pion pion scattering amplitude, Stanford Preprint ITP-1 (1964) non publié
  13. B. Bonnier, C Lopez et G.Mennessier, « Improved absolute bounds on the π0π0 amplitude », Physics Letters B, 60, (1), 22 December 1975, p. 63-66
  14. A. Martin, J.J. Loeffel, B. Simon, and A Wightman, « Padé: Approximants and the anharmonic oscillator », Phys, Leters, 30b, (1969), p. 656
  15. A.Martin, S.M. Roy, « Semi relativistic stability of systems with gravitationnal interactions », Phys Letters, b233 (1989), p. 409
  16. A.Martin, J.C.Raynal, S.M.Roy, J.Stubbe and V.Singh, « The Herbst Hamiltonian and the mass of boson stars », Phys. Letters, b320 (1994), p. 105
  17. A.Martin, B.B, Aumgartner et H Grosse, « Order of enertgy levels in potential models », Nuclear Physics, b254, (1985), p. 528
  18. A.Martin, « A simultaneous fit of bb, cc, ss, and cs spectra », Phys Letters, 100b, (1981), p. 511B
  19. J.M.Richard, « Nonperturbative quark dynamics in baryon », Phys. Letters, 100b, (1981), p. 515
  20. A.Martin et H, Grosse, Particle Physics and the Schrödinger equation, Cambridge University Press, 1997
  21. Status of Heavy Quark Systems, ArXiv:0705.2353v1{ hep-.th} 15 May 2007, unpublished
  22. A.Martin, J.M. Richard et T.T. Wu, « Stability of three unit-charge systems », Phys. Rev, a43, (1992), p. 3697
  23. A.Martin, A.Krikeb, J.M.Richard, et T.T. Wu, « On the stability domain of three arbirary charges », Few body systems, 29 (2000), p. 237
  24. A.Martin, K Chadan, N.N Khuri et T.T.Wu, « Universality of low energy scattering in 2+1 dimensions », Phys REVD58, (1998)
  25. A.Martin, T.T.Wu, « Bound states in 2 space dimensions in the non central case », Journ Math Phys, 45, (2004), p. 923
  26. A.Martin, S.M. Roy, « A lower bound on the inelastic cross-section for pion-pion scattering », Phys. Rev. D, 96 ( 2017), p. 114014
  27. A. Martin, T.T.Wu, « Positivity of the real part of the forward scattering amplitude », Phys. Rev D, 97 (2018), p. 014011
  28. A.Martin, H.Epstein, « A rigorous lower on the scattering amplitude at large angle, ArXiv », soumis à Physical Review, 2019 1903.00952 hep-th
  29. "Académie des sciences".
  30. "Un physicien du CERN reçoit la Médaille Gian Carlo Wick".
  31. "Le prix Pomeranchuk 2010 décerné à André Martin".
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