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

Biography After studying at the École normale supérieure (class of 1949), 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).Luc Allemand et Vincent Moncorgé, Les jardins de la physique, CNRS éditions, 2017, p. 38

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 shiftA. Martin et M.Gourdin., « Exact determination of a phenomenogical separable interaction », Nuovo Cimento, 11 (1959), p. 670 and an original demonstration of Levinson's theorem.A. Martin, « On the validity of the Levinson Theorem for non local interactions », Nuovo Cimento, 7, ( 1958), p. 607 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,A.Martin, J. Bowcock. A Mandelstam, « Representation for potential scattering », Nuovo Cimento, 14, ( 1959), p. 516 on the other hand a new method for studying partial waves using the Laplace transform.A.Martin, « Analyticity of partial waves obtained from the Schrödinger equation », Nuovo cimento, 14, (1959), p. 516

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,M.Froissart, « Asymptotic Behavior and Subtractions in the Mandelstam Representation », Phys. Rev, 123, (1961), p. 1053 he becomes interested in the amplitude of high-energy scattering. He demonstrates that Froissart's result for fixed-angle scattering can be improved.A.Martine, T.Kinoshita et J.J. Loeffel, « A new upper bound for fixed angle scattering amplitudes », Phys. Letters, 10, (1963), p. 460 Finally, in 1966, he succeeded in demonstrating the validity of the Froissart bound using local field theory, without postulating the Mandelstam representation.A.Martin, « Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity: », Nuovo Cimento, 42, (1966), p. 930 In the meantime, in 1964, he obtains an absolute bound on the pion-pion scattering amplitude,An absolute bound on the pion pion scattering amplitude, Stanford Preprint ITP-1 (1964) non publié this bound was considerably improved later.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

He also proved the convergence of Padé's approximates for the levels of the anharmonic oscillator.A. Martin, J.J. Loeffel, B. Simon, and A Wightman, « Padé: Approximants and the anharmonic oscillator », Phys. Letters, 30b, (1969), p. 656 He treated the relativistic effects on the instability of boson stars.A.Martin, S.M. Roy, « Semi relativistic stability of systems with gravitationnal interactions », Phys Letters, b233 (1989), p. 409A.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

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.A.Martin, B.B, Aumgartner et H Grosse, « Order of enertgy levels in potential models », Nuclear Physics, b254, (1985), p. 528 At the same time, in 1981, he proposed a naïve model of potential to reproduce the levels of quarkonium, whose predictive power is extraordinary.A.Martin, « A simultaneous fit of bb, cc, ss, and cs spectra », Phys Letters, 100b, (1981), p. 511B This model was also applied to baryons formed from 3 quarks with great success by Jean Marc Richard.J.M.Richard, « Nonperturbative quark dynamics in baryon », Phys. Letters, 100b, (1981), p. 515 An overview of these results can be found in the book written with H.GrosseA.Martin et H, Grosse, Particle Physics and the Schrödinger equation, Cambridge University Press, 1997 and a more recent unpublished review can be found in ArXives.Status of Heavy Quark Systems, ArXiv:0705.2353v1{ hep-.th} 15 May 2007, unpublished

He invented a geometrical method to study the stability of 3-body charged particle systems.A.Martin, J.M. Richard et T.T. Wu, « Stability of three unit-charge systems », Phys. Rev, a43, (1992), p. 3697A.Martin, A.Krikeb, J.M.Richard, et T.T. Wu, « On the stability domain of three arbitrary charges », Few body systems, 29 (2000), p. 237

André Martin has also studied low-energy scattering in the case of two dimensions of spaceA.Martin, K Chadan, N.N Khuri et T.T.Wu, « Universality of low energy scattering in 2+1 dimensions », Phys REVD58, (1998) as well as the counting of related states.A.Martin, T.T.Wu, « Bound states in 2 space dimensions in the non central case », Journ Math Phys, 45, (2004), p. 923

Recent work (after 2008) includes a lower bound on the inelastic rms cross-section,A.Martin, S.M. Roy, « A lower bound on the inelastic cross-section for pion-pion scattering », Phys. Rev. D, 96 ( 2017), p. 114014 the sign of the real part of the forward scattering amplitudA. Martin, T.T.Wu, « Positivity of the real part of the forward scattering amplitude », Phys. Rev D, 97 (2018), p. 014011 and a lower bound on the wide-angle scattering amplitude.A.Martin, H.Epstein, « A rigorous lower on the scattering amplitude at large angle, ArXiv », soumis à Physical Review, 2019 1903.00952 hep-th

Books

F. Cheung and A. Martin: Analyticity Properties and Bounds on Scattering 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 (, read online [archive]).

Awards

Doctor honoris Causa of the University of Lausanne, 1972. Corresponding member of the French Academy of sciences, 1980–2007. Chevalier of the Légion d'Honneur, 1992 Foreign Associate of the Indian Academy of Sciences Foreign Associate of the Tata Institute (Bombay) Gian-Carlo Wick Gold Medal, 2007 Pomeranchuk Prize, Moscow 2010.

References