GUILLOT Jean-Claude
Emeritus Professor
Address:
Ecole Polytechnique
Centre de Mathématiques Appliquées
UMR CNRS 7641
91198 PALAISEAU Cedex, FRANCE
Tél: 33 1 69 33 45 60
Fax: 33 1 69 33 46 46
Mail: jean-claude.guillot@polytechnique.edu
Research topics:
· Partial Differential Equations
· ScatteringTheory
· Inverse Problems
· Quantum Field Theory
Recent articles:
· The multipolar Hamiltonian in QED for moving atoms and ions . J.Phys.A:
Math.Gen., vol 35, p 5023-5039, 2002. (with J.Robert).
· Semiclassical asymptotics in magnetic Bloch bands. J.Phys.A: Math.Gen., Vol
35, p 7597-7605, 2002. (with M.Dimassi and J.Ralston)
· The Quantum Electrodynamics of Relativistic Bound States with Cutoffs.I.
Applied Mathematical Letters, vol 16, p 551-555, 2003. (with M.Dimassi).
· Quantum electrodynamics of relativistic bound states with
cutoffs.II. Contemporary Mathematics, vol 307, p 9-14, 2002.(with J.M.Barbaroux
and M.Dimassi).
· Quantum electrodynamics of relativistic bound states with cutoffs .Journal of
Hyperbolic Differential Equations, vol 1, p 271-314, 2004. (with J.M.Barbaroux and
M.Dimassi).
· On Effective Hamiltonians for Adiabatic Perturbations of Magnetic
Schrödinger Operators. Asymptotic Analysis, vol 40, p 137-146, 2004. (with
M.Dimassi and J.Ralston).
· Hierarchy of Multipolar Terms for Non Relativistic Moving Atoms in QED.
Preprint a rXiv: math-ph/0312009 and preprint mp-arc 03-513, 2003. (with A.Felhi
and J.Robert).
· Gaussian Beam Construction for Adiabatic Perturbations of Magnetic
Schrödinger Operators. Mathematical Physics, Analysis and Geometry, vol 9,
p.187-201, 2006. . (with M.Dimassi and J.Ralston).
· L’électron habillé non relativiste dans un champ
magnétique. C.R.Acad.Sci.Paris, Ser.I 340 p 421-426, 2005. (with L.Amour and
B.Grébert).
· The dressed nonrelativistic electron in a magnetic field. Math. Meth. Appl. Sci.,
vol 29, p 1121- 1146, 2006. (with L.Amour and B.Grébert).
· The dressed moving atoms and ions. J. Math. Pures Appl., vol 86, p 117- 200,
2006. (with L.Amour and B.Grébert ).
·A mathematical model for the Fermi weak interactions. Cubo 9, no 2, p 37-57,
2007. (with L.Amour and B.Grébert ).
· Organisation de la Journée Relativiste du Centre de Mathématiques
Appliquées de l'Ecole Polytechnique qui s'est tenue le 17 octobre 2007.
Intervenants: S. De Bièvre, C.Gérard, D. Häfner, Ph. LeFloch et M. Lewin.
· Le problème infrarouge pour l’électron habillé non relativiste dans un champ
magnétique. C.R.Acad. Sci.Paris Ser. I, 346, p 1045-1050, 2008. ( with L.Amour,
J.Faupin and B.Grébert )
· On the infrared problem for the dressed non-relativistic electron in a
magnetic field . Contemporary Mathematics 500, p 1-23, 2009. ( with L.Amour,
J.Faupin and B.Grébert ).
· Limiting absorption principle at low energies for a mathematical model of
weak interaction: the decay of a boson . C.R.Acad. Sci.Paris Ser. I, 347, p 1087-
1092, 2009. ((with J.-M. Barbaroux ).
· Spectral theory for a mathematical model of the weak interaction: the decay
of the intermediate vector bosons W+/- . Advances in Mathematical Physics, vol.
2009, Article ID 978903, 52 pages, 2009. See also arXiv: math-ph / 0904.3171. (
with J.-M. Barbaroux ).
· Spectral theory for a mathematical model of the weak interaction: the decay
of the intermediate vector bosons W+/- . II . Ann. Henri Poincaré, 12, p 1539-
1570, 2011. (with W. H. Aschbacher, J.-M. Barbaroux, J. Faupin).
· Corrigendum to "Inverse spectral theory for a singular Sturm- Liouville
operator on [0,1]". Journal of Differential. Eq., Volume 250 (2011),1232-1233.
(with J.Ralston).
· Organisation avec G. Allaire et J.-M. Barbaroux du colloque”Modèles
Mathématiques de la Théorie Quantique des Champs”. Centre de
Mathématiques Appliquées de l'Ecole Polytechnique les 7 et 8 décembre 2010.
Intervenants: Z.Ammari, V.Bach, L.Bruneau, T.Daudé, J.Faupin. V.Georgescu,
M.Griesemer, P.Indelicato, M.Lewin et A.Panati.
. Spectral Theory of a Mathematical Model in Quantum Field Theory for any
Spin. Preprint see arXiv: math-ph 1209.3207v1 (2012).
. Spectral theory of a mathematical model in quantum field theory for any spin. Spectral theory
and partial differential equations, 1337, Contemp. Math., 640, Amer. Math. Soc., Providence, RI,
2015.
. Spectral Theory near Thresholds for Weak Interactions with Massive Particles. Journal of
Spectral Theory, 6, (2016), 505555. (with J.-M. Barbaroux et J. Faupin).
. Spectral properties for Hamiltonians of weak interactions. Operator Theory: Advances and
Applications, 254 (2016), 1136. ( with J.-M. Barbaroux et J. Faupin).
. Local decay for weak interactions with massless paticles. arXiv : 1611.07814. A paraître dans
Journal of Spectral Theory. (with J.-M. Barbaroux et J. Faupin).
. A mathematical model of weak interactions in a background of a uniform magnetic field.I. The
inverse β decay. <hal-01585239> and mp-arc :18-35. 2017.
. Weak Interactions in a Background of a Uniform Magnetic Field. A Mathematical Model for
the Inverse Beta Decay.I. Open Access Library Journal, 4, e4142.2017.
doi: http://dx.doi.org/10.4236/oalib.1104142.
En Préparation
. Mathematical models for the weak interactions for charged and neutral fermions with
anomalous magnetic moments in uniform magnetic field.
. Etude spectrale des opérateurs de Dirac non autoadjoints.
Récents exposés donnés dans des conférences internationales :
.ESI Vienna program on "Matter and Radiation", which has taken place at the Erwin
Schroedinger International Institute in Vienna from May 3 until July 30, 2010.
.Journée Thématique. Laboratoire AGM. Mathematical Aspects of Quantum Field Theory. Le
18 mars 2013 à l’Université de Cergy Pontoise.
.Conférence en l’honneur de J.Ralston à UCLA du 17 au 21 juin 2013.
.Conférence en l’honneur de L. Halpern à l’Institut Henri Poincaré du 20 au 22 janvier 2014.