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| | 50 yrs old Upholsterer Corredor from Brome, loves to spend time renting movies, ganhando dinheiro na internet and flower arranging. Will shortly undertake a contiki tour that may incorporate traveling to the Historic Town of Zabid.<br><br>Also visit my site: [http://comoganhardinheironainternet.comoganhardinheiro101.com ganhar dinheiro] |
| {{Infobox scientist
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| | name = Maurice de Gosson
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| | image = Maurice.charlyne.degosson.png
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| | image_size =
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| | caption = Maurice and Charlyne de Gosson
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| | birth_date = {{birth date|1948|03|13|df=y}}
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| | birth_place = [[Berlin]], [[Germany]]
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| | residence = [[Vienna]], [[Austria]]
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| | field = [[Harmonic analysis]], [[Symplectic geometry]],<br>[[Quantum mechanics]]
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| | alma_mater = [[University of Nice]]<br>[[University of Paris 6]]
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| | known_for = Applications of the principle of the symplectic camel to physics
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| | spouse = Charlyne de Gosson
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| }}
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| '''Maurice A. de Gosson''' (born 13 March 1948), (also known as Maurice Alexis de Gosson de Varennes) is an [[Austria]]n mathematician and mathematical physicist, born in 1948 in Berlin.<ref>Biography at the NuHAG website – University of Vienna, ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref> He is currently a Senior Researcher at the Numerical Harmonic Analysis Group (NuHAG)<ref>Numerical Harmonic Analysis Group website, University of Vienna ([http://www.univie.ac.at/nuhag-php/home/])</ref> of the [[University of Vienna]].<ref>Homepage at the NuHAG website – University of Vienna, ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref>
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| == Work ==
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| After completing his PhD in [[microlocal analysis]] at the University of Nice in 1978 under the supervision of [[Jacques Chazarain]], de Gosson soon became fascinated by [[Jean Leray]]'s [[Lagrangian analysis]]. Under Leray's tutorship de Gosson completed a Habilitation à Diriger des Recherches en Mathématiques at the University of Paris 6 (1992). During this period he specialized in the study of the [[Leray–Maslov index]] and in the theory of the [[metaplectic group]], and their applications to mathematical physics. In 1998 de Gosson met [[Basil Hiley]], who triggered his interest in conceptual question in [[quantum mechanics]]. Basil Hiley wrote a foreword to de Gosson's book ''The Principles of Newtonian and Quantum Mechanics'' (Imperial College Press, London).
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| After having spent several years in Sweden as Associate Professor and Professor in Sweden, de Gosson was appointed in 2006 at the Numerical Harmonic Analysis Group of the University of Vienna, created by [[Hans Georg Feichtinger]] (see www.nuhag.eu). He currently works in symplectic methods in harmonic analysis, and on conceptual questions in quantum mechanics, often in collaboration with Basil Hiley.<ref>University website, short biography – 2011 ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref><ref>University website, Research section([http://homepage.univie.ac.at/maurice.de.gosson/research.htm])</ref>
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| == Visiting positions ==
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| Maurice de Gosson has held longer visiting positions at [[Yale University]]
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| ,<ref>AMS.org - Mathematics Calendar([http://www.ams.org/notices/199801/people.pdf])</ref><ref>IOPscience, ip.org ([http://iopscience.iop.org/0305-4470/31/18/013])</ref> [[University of Colorado]] in [[Boulder]] (Ulam Visiting Professor)
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| ,<ref>AMS.org - Mathematics Calendar([http://www.ams.org/notices/199906/mathcal.pdf])</ref> [[University of Potsdam]], [[Albert-Einstein-Institut]] (Golm), [[Max-Planck-Institut für Mathematik]] ([[Bonn]]), [[Université Paul Sabatier]] ([[Toulouse]]), [[Jacobs Universität]] ([[Bremen]])
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| == The symplectic camel ==
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| Maurice de Gosson was the first to prove that [[Mikhail Leonidovich Gromov|Mikhail Gromov]]'s symplectic [[non-squeezing theorem]] (also called „the Principle of the Symplectic Camel“) allowed the derivation of a classical uncertainty principle formally totally similar to the [[Robertson–Schrödinger uncertainty relations]] (i.e. the [[Heisenberg inequalities]] in a stronger form where the covariances are taken into account).<ref>Reich, New Scientist – ([http://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html]), 2009</ref> This rather unexpected result was discussed in the media.<ref name="www.newscientist.com">{{Cite web | last = Samuel Reich| first = Eugenie | title = How camels could explain quantum uncertainty | url = http://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html | publisher = New Scientist | date = 26 February 2009 | accessdate = 18 December 2013 }}</ref>
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| == Quantum blobs ==
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| In 2004/2005,<ref>M. de Gosson (2004), Phys. Lett. A, vol. 330, pp. 161 ff., and M. de Gosson (2005), Bull. Sci. Math., vol. 129, pp. 211, both cited according to M. de Gosson (2005), ''Symplectically covariant Schrödinger equation in phase space'', ''Journal of Physics A, Mathematics and General'', vol. 38, pp. 9263-9287 (2005)</ref> de Gosson showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by ''symplectic quantum cells'', each described by a mean momentum and a mean position. The cell is invariant under [[canonical transformation]]s. De Gosson called such a quantum cell a ''quantum blob'':
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| :The quantum blob is the image of a phase space ball with radius <math>\sqrt{ \hbar }</math> by a (linear) [[symplectic transformation]].<ref name="de-gosson-2004-0407129v1">Maurice A. de Gosson: ''On the goodness of "quantum blobs" in phase space quantization'', [http://arxiv.org/abs/quant-ph/0407129v1 arXiv:quant-ph/0407129v1], submitted 16 July 2004 (however, dated February 1, 2008)</ref>
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| and
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| :“Quantum blobs are the smallest phase space units of phase space compatible with the [[uncertainty principle]] of quantum mechanics and having the [[symplectic group]] as group of symmetries. Quantum blobs are in a bijective correspondence with the [[squeezed coherent states]] from standard quantum mechanics, of which they are a phase space picture.”<ref name="de-gosson-2011-quantum-blobs">Maurice A. de Gosson: ''Quantum blobs'', [http://arxiv.org/abs/1106.5468v1 http://arxiv.org/abs/1106.5468v1], submitted 27 June 2011</ref>
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| Their invariance property distinguishes de Gosson's quantum blobs from the "quantum cells" known in thermodynamics, which are units of phase space with a volume of the size of Planck's constant ''h'' to the power of 3.<ref>[http://www.freewebs.com/cvdegosson/thesymplecticcamel.htm The symplectic camel: the tip of an iceberg?], website of Maurice A. de Gosson, downloaded October 5, 2012</ref><ref>M. A. de Gosson: ''The Principles of Newtonian & Quantum Mechanics: The Need for Planck's Constant, h'', Imperial College Press, 2001, ISBN 978-1860942747, p. 120</ref>
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| == Influence ==
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| De Gosson's notion of quantum blobs has given rise to a proposal for a new formulation of quantum mechanics, which is derived from postulates on quantum-blob-related limits to the extent and localization of quantum particles in phase space;<ref name="de-gosson-2011-quantum-blobs"/><ref>D. Dragoman: ''Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem'', 2005 Physica Scripta, vol. 72, no. 2, pp. 290–295, {{DOI|10.1238/Physica.Regular.072a00290}}, [http://arxiv.org/abs/quant-ph/0402100 arXiv:quant-ph/0402100] submitted 16 February 2004</ref> this proposal is strengthened by the development of a phase space approach that applies to both quantum and classical physics, where a quantum-like evolution law for observables can be recovered from the classical Hamiltonian in a non-commutative phase space, where ''x'' and ''p'' are (non-commutative) c-numbers, not operators.<ref>D. Dragoman: ''Quantum-like classical mechanics in non-commutative phase space'', Proceedings of the Romanian Academy, Series A, vol. 12, no. 2/2011, pp. 95–99 ([http://www.acad.ro/sectii2002/proceedings/doc2011-2/03-Dragoman.pdf full text])</ref>
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| == Publications ==
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| === Books ===
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| [[File:Symplectic Geometry and Quantum Mechanics.jpg|thumb|Symplectic Geometry and Quantum Mechanics (2006)]]
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| * Symplectic Methods in Harmonic Analysis and Applications to Mathematical Physics; Birkhäuser (2011)<ref name="springer.com">Springer, ([http://www.springer.com/?SGWID=0-102-24-0-0&searchType=EASY_CDA&queryText=de+Gosson])</ref> ISBN 3-7643-9991-0
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| * Symplectic Geometry and Quantum Mechanics. Birkhäuser, Basel, series "Operator Theory: Advances and Applications" (2006)<ref name="springer.com"/> ISBN 3-7643-7574-4
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| * The Principles of Newtonian and Quantum Mechanics: the Need for Planck's Constant h; with a foreword by B. Hiley. Imperial College Press (2001) ISBN 1-86094-274-1
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| *Maslov Classes, Metaplectic Representation and Lagrangian Quantization. Mathematical Research 95, Wiley VCH (1997), ca 190 pages ISBN 3-527-40087-7
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| * In preparation: Mathematical and Physical Aspects of Quantum Processes (with Basil Hiley)
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| * In preparation: Pseudo-Differential operators and Quantum Mechanics
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| === Selected recent papers ===
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| * The symplectic egg. [http://arxiv.org/abs/1208.5969v1 arXiv:1208.5969v1], to appear in American Journal of Physics (2013)
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| * Symplectic Covariance Properties for Shubin and Born Jordan Pseudo-Differential Operators. Trans. Amer. Math. Soc. (2012) (abridged version: [http://arxiv.org/abs/1104.5198v1 arXiv:1104.5198v1] submitted 27 April 2011)
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| * A pseudo-differential calculus on non-standard symplectic space; Spectral and regularity results in modulation spaces. Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, November 2011, Pages 423-445<ref>Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, ([http://www.sciencedirect.com/science/journal/00217824])</ref>
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| * (With B. Hiley) Imprints of the Quantum World in Classical Mechanics. Foundations of Physics (26 February 2011), pp. 1–22, {{doi|10.1007/s10701-011-9544-5}} ([http://www.springerlink.com/content/qn76575r55543453 abstract], [http://arxiv.org/abs/1001.4632 arXiv:1001.4632] submitted 26 January 2010, version of 15 December 2010)
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| * (with F. Luef) Preferred quantization rules: Born-Jordan versus Weyl. The pseudo-differential point of view. J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, 115–139<ref>J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=291105])</ref>
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| * (with N. Dias F. Luef, J. Prata, João) A deformation quantization theory for noncommutative quantum mechanics. J. Math. Phys. 51 (2010), no. 7, 072101, 12 pp.
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| * (with F. Luef) Symplectic capacities and the geometry of uncertainty: the irruption of symplectic topology in classical and quantum mechanics.Phys. Rep. 484 (2009), no. 5, 131–179<ref>Phys. Rep. 484 (2009), no. 5, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=278137])</ref>
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| * The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 39 (2009), no. 2, 194–214<ref>Found. Phys. 39 (2009), no. 2, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/journaldoc.html?cn=Found_Phys])</ref>
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| * On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths. J. Math. Pures Appl. (9) 91(2009), no. 6, 598–613.<ref>J. Math. Pures Appl. (9) 91(2009), no. 6, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=274281])</ref>
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| * Spectral properties of a class of generalized Landau operators. Comm. Partial Differential Equations 33 (2008), no. 10-12, 2096–2104
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| * Metaplectic representation, [[Conley–Zehnder index]], and [[Weyl calculus]] on [[phase space]]. Rev. Math. Phys. 19 (2007), no. 10, 1149–1188.
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| * Symplectically covariant Schrödinger equation in phase space. Journal of Physics A, vol. 38 (2005), no. 42, pp. 9263, {{DOI|10.1088/0305-4470/38/42/007}}, [http://arxiv.org/abs/math-ph/0505073v3 arXiv:math-ph/0505073v3] submitted 27 May 2005, version of 30 July 2005
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| == References ==
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| {{Reflist}}
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| == External links ==
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| * [http://www.freewebs.com/cvdegosson/ Personal homepage]
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| * Lectures:
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| ** M. de Gosson, [[Basil Hiley|B. Hiley]]: [http://www.freewebs.com/cvdegosson/TalkBileyFest.pdf Zeno paradox for Bohmian trajectories: The unfolding of the metatron], November 2010
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| ** Maurice A. de Gosson: [http://www.freewebs.com/cvdegosson/Oxford2010.pdf Imprints of classical mechanics in the quantum world. Schrödinger equation and the uncertainty principle], October 2010
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| * http://books.google.at/books/about/Symplectic_Geometry_And_Quantum_Mechanic.html?id=q9SHRvay75IC&redir_esc=y
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| * http://iopscience.iop.org/0305-4470/34/47/313/
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| * http://rd.springer.com/article/10.1007/s10701-009-9272-2
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| * http://www.amazon.com/Metaplectic-Representation-Lagrangian-Quantization-Mathematical/dp/3527400877
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| * http://adsabs.harvard.edu/abs/2007RvMaP..19.1149D
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| * http://rd.springer.com/article/10.1007/s11005-007-0150-6
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| * http://iopscience.iop.org/0305-4470/36/48/L01/
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| * http://rd.springer.com/article/10.1007/s11005-008-0261-8
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| * http://rd.springer.com/article/10.1007/s10455-008-9106-z
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| * http://adsabs.harvard.edu/abs/2011arXiv1106.5468D
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| * http://adsabs.harvard.edu/abs/2004quant.ph..7129D
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| * https://www.interllective.com/arxiv/article/1106.5468
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| * https://www.researchgate.net/publication/51968170_The_Reconstruction_Problem_and_Weak_Quantum_Values
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| {{Persondata
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| | NAME = Gosson, Maurice A. De
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Austrian mathematician
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| | DATE OF BIRTH = 13 March 1948
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| | PLACE OF BIRTH = [[Berlin]], [[Germany]]
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Gosson, Maurice A. De}}
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| [[Category:Articles created via the Article Wizard]]
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| [[Category:Austrian mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:1948 births]]
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| [[Category:Living people]]
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