Maurice A. de Gosson, is an Austrian mathematician and mathematical physicist, born in 1948 in Berlin. He is currently a Senior Researcher at the Numerical Harmonic Analysis Group of the University of Vienna.
Work
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. 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. 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. He currently works in symplectic methods in harmonic analysis, and on conceptual questions in quantum mechanics, often in collaboration with Basil Hiley.
In 2003, Gosson introduced the notion of quantum blobs, which are defined in terms of symplectic capacities and are invariant under canonical transformations. Shortly after, he showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by such quantum blobs, each described by a mean momentum and a mean position: and 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. Together with G. Dennis and Basil Hiley, de Gosson laid out examples of how the quantum blob can be seen as a "blow-up" of a particle in phase space. To demonstrate this, they picking up on “Fermi's trick” which allows to identify an arbitrary wavefunction as a stationary state for some Hamiltonian operator. They showed that this blow-up requires internal energy that comes from the particle itself, involving the kinetic energy and David Bohm's quantum potential. In the classical limit, the quantum blob becomes a point particle.
Influence
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; 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 c-numbers, not operators.
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
Preferred quantization rules: Born-Jordan versus Weyl. The pseudo-differential point of view. J. Pseudo-Differ. Oper. Appl. 2, no. 1, 115–139
A deformation quantization theory for noncommutative quantum mechanics. J. Math. Phys. 51, no. 7, 072101, 12 pp.
Symplectic capacities and the geometry of uncertainty: the irruption of symplectic topology in classical and quantum mechanics.Phys. Rep. 484, no. 5, 131–179
The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 39, no. 2, 194–214
On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths. J. Math. Pures Appl. 91, no. 6, 598–613.
Spectral properties of a class of generalized Landau operators. Comm. Partial Differential Equations 33, no. 10-12, 2096–2104
Symplectically covariant Schrödinger equation in phase space. Journal of Physics A, vol. 38, no. 42, pp. 9263,, submitted 27 May 2005, version of 30 July 2005
