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List of publications of Maurice de Gosson

127. M. de Gosson, Quantum Polar Duality and the Symplectic Camel: a New Geometric Approach to Quantization. To appear in Found. Phys. (2021)

126. M. de Gosson, Gaussian Quantum States Can Be Disentangled Using Symplectic Rotations. To appear in Lett. Math. Phys. (2021)

125. M. de Gosson, On the Disentanglement of Gaussian Quantum States by Symplectic Rotations. C.R. Acad. Sci. Paris Volume 358, issue 4,  459462 (2020)

124. M. de Gosson, On Density Operators with Gaussian Weyl symbols, In: Advances in Microlocal and Time-Frequency Analysis, Springer (2020)

123. M. de Gosson, Symplectic Coarse-Grained Classical and Semclassical Evolution of Subsystems: New Theoretical Aspects,  J. Math. Phys. no. 9, 092102 (2020)

122. M. de Gosson, Symplectic Coarse-Grained Dynamics: Chalkboard Motion in Classical and Quantum Mechanics,  Adv. Theor. Math. Phys. 24(4) (2020) arXiv:1901.06554v1

121. E. Cordero, M. de Gosson, and F. Nicola, A characterization of modulation spaces by symplectic rotations, to appear in J. Funct. Anal. (2020) , arXiv:1707.06862v1 [math.FA]

120. E. Cordero, M. de Gosson, M. Dörfler, and F. Nicola, Generalized Born-Jordan Distributions and Applications, to appear in  Advances in Computational Mathematics (ACOM) (2020)

119. M. de Gosson and F. Luef, Moyal Bracket and Ehrenfest's Theorem in Born-Jordan Quantization, Quantum Reports 1(1), 71-81 (2019)

118. B. Koczor, F. vom Ende, M. de Gosson, S. J. Glaser, and Robert Zeier, Phase Spaces, Parity Operators, and the Born-Jordan Distribution,  arXiv:1811.05872 [quant-ph]

117  E. Cordero, M. de Gosson, and F. Nicola, On the Positivity of Trace Class Operators, Advances in Theoretical and Mathematical Physics (2019) [in print] arXiv:1706.06171 [math.FA]

116. M. Faulhuber, M.A. de Gosson, D. Rottensteiner, Gaussian Distributions and Phase Space Weyl-Heisenberg Frames, arXiv:1708.01 [to appear in Appl. Comput. Harmon. Anal. (2018)]

115. M. de Gosson and J. Toft, Continuity properties for Born--Jordan operators with symbols in Hörmander classes and modulation spaces.  Acta Math. Sci. Ser. B (Engl. Ed.) 40(6), 1603-1626 (2020) 

114. N. Dias, M. de Gosson, and J. Prata, A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions, J. Fourier Anal. Appl. 25(1), 210-241 (2019)

113. M. de Gosson, On Density Operators with Gaussian Weyl Symbols, in Proceedings to the Conference MLTFA18 - Microlocal and Time-Frequency Analysis. Birkhäuser, series Applied Numerical and Harmonic Analysis (series editor: John J. Benedetto), 2018

112. M. de Gosson, On the Purity and Entropy of Mixed Gaussian States, in Landscapes of Time-Frequency Analysis, eds. Boggiatto, Paolo, Elena Cordero, Maurice de Gosson, Hans G. Feichtinger, Fabio Nicola, Alessan Oliaro, and Anita Tabacco. Springer Nature, 2019

111. M. de Gosson, The Symplectic Camel and Poincaré Superrecurrence: Open Problems, Entropy 20(7), 499 (2018)

110. B.J. Hiley, M.A. de Gosson and G. Dennis, Quantum Trajectories: Dirac, Moyal and Bohm. Quanta (2019), ArXiv:1610.07130v1 [quant-ph]

109. M. de Gosson, Short-Time Propagators and the Born--Jordan Quantization Rule [invited contribution], Entropy 20(11), 869 (2018)

108. M. de Gosson, Quantum Harmonic Analysis of the Density Matrix, Quanta 7, 74-110 (2018)

107. M. de Gosson and F. Nicacio, Relative Phase Shifts for Metaplectic Isotopies Acting on Mixed Gaussian States, J. Math. Phys. 59(5), 052106 (2018) [arXiv:1802.07499v2]

106. E. Cordero, M. de Gosson, M. Dörfler, and F. Nicola, On the symplectic covariance and interferences of time-frequency distributions, SIAM J. Math. Anal. 50(2), 2178--2193 (2018)

105. E. Cordero, M. de Gosson, and F. Nicola, On the reduction of the interferences in the Born--Jordan distribution, Appl. Comput. Harmon. Anal. 44(2), 230--245 (2018)

104. M. de Gosson and F. Nicola, Born--Jordan pseudodifferential operators and the Dirac correspondence: beyond the Groenewold--van Hove Theorem. Bull. Sci. Math. 144, 64-81 (2018)

102. M. de Gosson, Mixed Quantum States with Variable Planck Constant, Phys. Lett. A 381(36), 3033-3037 (2017)

101. E. Cordero, M. de Gosson, and F. Nicola, Semi-classical Time-frequency Analysis and Applications, Math. Phys. Anal. Geom. 20(26) (2017)

100. E. Cordero, M. de Gosson, and F. Nicola, Quantum Harmonic Analysis and the Positivity of Trace Class Operators; Applications to Quantum Mechanics. In: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science, vol 10589. Springer, Cham, 2017

99. E. Cordero, M. de Gosson, and F. Nicola, On the Invertibility of Born-Jordan Quantization, J. Math. Pures Appl. 05(4) 537-557 (2016)

98. E. Cordero, M. de Gosson, F. Nicola, Born--Jordan pseudo-differential operators with symbols in the Shubin classes, Trans. Amer. Math. Soc. (Series B4), 94-109 (2017)

97. M. de Gosson, The angular momentum dilemma and Born--Jordan quantization. Found. Phys. 47(1), 61-70 (2017)

96. M. de Gosson, The Canonical Group of Transformations of a Weyl--Heisenberg Frame; Applications to Gaussian and Hermitian Frames, J. Geom. Phys. 114, 375-383 (2017)

95. M. de Gosson, Two Geometric Interpretations of the Multidimensional Hardy Uncertainty Principle. Appl. Comput. Harmon. Anal. 42(1), 143-153 (2017)

94. E. Cordero, M. de Gosson, and F. Nicola, Time-frequency analysis of Born--Jordan pseudodifferential operators, J. Funct. Anal. 272(2), 577-598 (2017)

93. M. de Gosson, Bypassing the Groenewold--van Hove obstruction on R²ⁿ: a new argument in favor of Born-Jordan quantization. J. Phys.A: Math. Gen. 49(39), 39LT01 (2016)

92. M. de Gosson, B. Hiley, and E. Cohen, Observing Quantum Trajectories: From Mott's Problem to Quantum Zeno Effect and Back. Ann. Phys. 374, 190-211 (2016)

91. M. de Gosson, K. Gröchenig, and J. L. Romero, Stability of Gabor Frames under Small-Time Hamiltonian Evolution, Lett. Math. Phys. 106(6), 799-809 (2016)

90. M. de Gosson and F. Luef, Born--Jordan Pseudodifferential Calculus, Bopp Operators and Deformation Quantization, Integral Equations Operator Theory 84(4), 463-485 (2016)

89. M. de Gosson, From Weyl to Born--Jordan Quantization: The Schrödinger Representation Revisited. Phys. Reps. 623, 1-58 (2016)

88. C. de Gosson and M. de Gosson, Weak Values, the Reconstruction Problem, and the Uncertainty Principle, EmQM15: Emergent Quantum Mechanics 2015 IOP Publishing Journal of Physics: Conference Series 701, 012011 (2016)

87. C. de Gosson and M. de Gosson, The Phase Space Formulation of Time-Symmetric Quantum Mechanics, Quanta 4(1) (2015)

86. L. D. Abreu, P. Balazs, M. de Gosson, and Z. Mouayn, Discrete coherent states for higher Landau levels, Ann. Phys. 363, 337-353 (2015)

85. M. de Gosson, Paths of Canonical Transformations and their Quantization. Rev. Math. Phys. 27(6), 1530003 (2015)

84. M. de Gosson, Quantum Indeterminacy and Polar Duality, Math. Phys. Anal. Geom. 18(1) 1-10 (2015)

83. G. Dennis, M. de Gosson, and B. Hiley, Bohm's Quantum Potential as an Internal Energy. Phys. Lett. A 379(18) 1224-1227 (2015)

82. M. de Gosson, Born--Jordan Quantization and the Equivalence of the Schrödinger and Heisenberg Pictures. Found. Phys. 44(10), 1096-1106 (2014)

81. G. Dennis, M. de Gosson, and B. Hiley, Fermi's Ansatz and Bohm's Quantum Potential. Phys. Lett.A 378(32), 2363-2366 (2014)

80. M. de Gosson and B. Hiley, Hamiltonian flows, short-time propagators and the quantum Zeno effect. EmQM13: Emergent Quantum Mechanics 2013 IOP Publishing, Journal of Physics: Conference Series 504 (2014)

79. M. de Gosson, Hamiltonian deformations of Gabor frames: First steps. Appl. Comput. Harmon. Anal. 38(2), 196-221 (2014)

78. M. de Gosson, and F. Luef, Metaplectic Group, Symplectic Cayley Transform, and Fractional Fourier Transforms, J. Math. Anal. and Appl. (2014)

77. N. Dias, M. de Gosson, and J. Prata, Metaplectic Formulation of the Wigner Transform and Applications, Rev. Math. Phys. 25(10), 1343010, (2013)

76. M. de Gosson, and B. Hiley, Hamiltonian Flows and the Holomovement, Mind and Matter (2013) 11(2) 205-221 (2013)

75. M. de Gosson, The Symplectic Camel and Quantum Universal Invariants: The Angel of Geometry versus the Demon of Algebra, Quantum Matter, 1 Vol. 3, no. 3 (2013)

74. N. Dias, M. de Gosson, J. Prata, Maximal covariance group of Wigner transforms and pseudo-differential operators. Proc. Amer. Math. Soc. 142(9), 3183-3192 (2014)

73. M. de Gosson, D. Scheeres, and J. Maruskin, Applications of Symplectic Topology to Orbit Uncertainty and Spacecraft Navigation. J. of Astronaut. Sci. 59(1-2), 63-83 (2012)

72. M. de Gosson, Born--Jordan Quantization and the Uncertainty Principle. J. Phys. A: Math. Theor. 46 (2013)

71. M. de Gosson, The symplectic egg in quantum and classical mechanics. Amer. J. of Phys. 81(5) (2013)

70. E. Binz, M. de Gosson, and B. Hiley, Clifford algebras in symplectic geometry and quantum mechanics. Found. Phys. 43(4), 424-439 (2013)

69. N. Dias, M. de Gosson, J. Prata, A symplectic extension map and a new Shubin class of pseudo-differential operators. J. Funct. Anal. 266(6), 3772-3796 (2014)

68. M. de Gosson and E. Pauwels, On the prolate spheroidal wave functions and Hardy's uncertainty principle. J. Fourier Anal. Appl. 3, 566-576 (2014)

67. M. de Gosson, Quantum blobs. Found. Phys. 43(4), 440-457 (2013)

66. M. de Gosson and B. Hiley, Short-Time Quantum Propagator and Bohmian Trajectories. Phys. Lett. A. 377(42), 6 (2013)

65. M. de Gosson, Symplectic Covariance Properties for Shubin and Born--Jordan Pseudo-Differential Operators. Trans. Amer. Math. Soc. 365, 3287-3307 (2013)

64. M. de Gosson, On the partial saturation of the uncertainty relations of a mixed Gaussian state. J. Phys. A 45(41) (2012)

63. M. de Gosson and D. Abreu, Weak values and Born-Jordan quantization. AIP Conf. Proc. 156 (2012)

62. N. Dias, M. de Gosson, J. Prata, Quantum mechanics in phase space: the Schrödinger and the Moyal representations. J. Pseudo-Differ. Oper. Appl. 3(4) ( 2012)

61. M. de Gosson, A Pseudo-Quantum Triad: Schrödinger's Equation, the Uncertainty Principle, and the Heisenberg Group. J. Phys.: Conf. Ser. 361 (2012)

60. M. de Gosson, and S. de Gosson, Weak values of a quantum observable and the cross-Wigner distribution. Phys. Lett. A 376(4), 293--296 (2012)

60.M. de Gosson and S. de Gosson, The reconstruction problem and weak quantum values. J. Phys. A 45(11) (2012)

59. N. Dias, M. de Gosson, J. Prata, A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces. J. Math. Pures Appl. 9 96 (2011)

58. M. de Gosson and F. Luef, Preferred Quantization Rules: Born--Jordan vs. Weyl; Applications to Phase Space Quantization. J. Pseudo-Differ. Oper. Appl. 2(1) (2011)

57. M. de Gosson, On the Transformation Properties of the Wigner Function Under Hamiltonian Symplectomorphisms. J. Pseudo-Differ. Oper. Appl. 2(1) (2011)

56. M. de Gosson and B. Hiley, Imprints of the Quantum World in Classical Mechanics. Found. Phys. 41(9) (2011)

55. M. de Gosson, On the Use of Minimum Volume Ellipsoids and Symplectic Capacities for Studying Classical Uncertainties for Joint Position-Momentum Measurements. J. Stat. Mech.: Theory and Experiment 11, P11005 (2010)

54. M. de Gosson and F. Luef, Spectral and Regularity properties of a Pseudo-Differential Calculus Related to Landau Quantization. J. Pseudo-Differ. Oper. Appl. 1(1) (2010)

53. N. Dias, M. de Gosson, F. Luef, and J. Prata, A Deformation Quantization Theory for Non-Commutative Quantum Mechanics. J. Math. Phys. 51 (2010)

52. M. de Gosson, A pseudodifferential calculus on non-standard symplectic space. Appl. Anal. 90(11), 1-12, (2011)

51. M. de Gosson, The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg? Found. Phys. 39(2), 194-214 (2009)

50. M. de Gosson, On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths. J. Math. Pures Appl. 91 (2009)

49. M. de Gosson and F. Luef, On the usefulness of modulation spaces in deformation quantization. J. Phys. A: Math. Theor. 42(31), 315205 (2009)

48. M. de Gosson and F. Luef, Symplectic Capacities and the Geometry of Uncertainty: the Irruption of Symplectic Topology in Classical and Quantum Mechanics. Phys. Reps. 484, 131-179 (2009)

47. M. de Gosson, Spectral Properties of a Class of Generalized Landau Operators. Comm. Partial Diff. Equations 33(11) (2008)

46. M. de Gosson and F. Luef, A new approach to the ⋆-genvalue equation. Lett. Math. Phys. 85 (2008)

45. M. de Gosson, Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators (Invited paper). In Recent Developments in Pseudo-Differential Operators 2008/09 in the Birkhäuser series "Operator Theory: Advances and Applications". Preprint available at:

44. M. de Gosson, S. de Gosson, P. Piccione, On a product formula for the Conley-Zehnder index of symplectic paths and its applications. Ann. Glob. Anal. Geom. 34 (2008)

43. M. de Gosson, Semi-Classical Propagation of Wavepackets for the Phase Space Schrödinger Equation; Interpretation in Terms of the Feichtinger Algebra. J. Phys.A: Math. Theor. 41 (2008)

42. M. de Gosson and F. Luef, Principe d'Incertitude et Positivité des Opérateurs à Trace; Applications aux Opérateurs Densité. Ann. H. Poincaré 9(2) (2008)

41. M. de Gosson, Metaplectic Representation, Conley--Zehnder Index, and Weyl Calculus on Phase Space. Rev. Math. Physics, 19(8) (2007)

40. M. de Gosson and F. Luef, Quantum States and Hardy's Formulation of the Uncertainty Principle: a Symplectic Approach. Lett. Math. Phys. 80 (2007)

39. M. de Gosson and J. Isidro, Abelian Gerbes as a Gauge Theory of Quantum Mechanics on Phase Space. J. Phys. A: Math. Theor. 40 (2007)

38. M. de Gosson and J. Isidro, A Gauge Theory of Quantum Mechanics. Modern Physics Letters A, 22(3) (2007)

37. M. de Gosson and F. Luef, Remarks on the fact that the uncertainty principle does not characterize the quantum state. Phys. Lett. A. 364 (2007)

36. M. de Gosson and S. de Gosson, An extension of the Conley--Zehnder Index, a product formula and an application to the Weyl representation of metaplectic operators. J. Math. Phys. 47 (2006)

35. M. de Gosson, Schrödinger Equation in Phase Space, Irreducible Representations of the Heisenberg Group, and Deformation Quantization. Resenhas 6(4) (2006)

34. M. de Gosson, Weyl Calculus in Phase Space and the Torres-Vega and Frederick Equation, Quantum theory: reconsideration of foundations. AIP Conf. Proc. 3(810) Amer. Inst. Phys. (2006)

33. M. de Gosson, The adiabatic limit for multi-dimensional Hamiltonian systems; Journ. Geom. and Symmetry in Physics 4 (2005-2006)

32. M. de Gosson, Uncertainty principle, phase space ellipsoids, and Weyl calculus. Operator Theory: Advances and applications, Vol. 164, Birkhäuser Verlag, Basel (2006)

31. M. de Gosson, Symplectically Covariant Schrödinger Equation in Phase Space. J. Phys.A:Math. Gen. 38(42) (2005)

30. M. de Gosson, Cellules quantiques symplectiques et fonctions de Husimi-Wigner. Bull. Sci. Math. 129 (2005)

29. M. de Gosson, Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation. J. Phys. A 38(19) (2005)

28. M. de Gosson, The Weyl Representation of Metaplectic operators. Lett. Math. Phys. 72 (2005)

27. M. de Gosson, The optimal pure Gaussian state canonically associated to a Gaussian quantum state. Phys. Lett. A 330(3-4) (2004)

26. M. de Gosson, On the notion of phase in mechanics. J. Phys. A: Math. Gen. 37(29) (2004)

25. M. de Gosson, The Maslov Index indices of Periodic Hamiltonian Orbits. J. Phys. A:Math. Gen. 36(48) (2003)

24. M. de Gosson and S. de Gosson, Phase Space Quantization and the Uncertainty Principle. Phys. Lett. A 317(5-6) (2003)

23. M. de Gosson, On probability waves in classical and quantum mechanics, in Växjö Conference on Quantum Mechanics, World Scientific, 2003

22. M. de Gosson and S. de Gosson, The cohomological interpretation of the indices of Robbin and Salamon. Jean Leray ´99 Conference Proceedings. Math. Phys. Studies 4, Kluwer Academic Press (2003)

21. M. de Gosson, A class of symplectic ergodic adiabatic invariants. Foundations of probability and physics, 2 (Växjö, 2002) 151-158. Växjö Univ. Press, Växjö (2003)

20. M. de Gosson and S. de Gosson, Symplectic path intersections and the Leray index. Symplectic path intersections and the Leray index. Partial differential equations and mathematical physics (Tokyo, 2001), Progr. Nonlinear Differential Equations Appl. 52, Birkhäuser Boston, Boston, MA (2003)

19. M. de Gosson, The "symplectic camel principle" and semiclassical mechanics, J. Phys. A: Math. Gen. 35(3) (2002)

18. M. de Gosson and S. de Gosson, Fonctions d'ondes semi-classiques et équations de Schrödinger; in Partial Differential Equations and Mathematical Physics, Marcel Dekker (2002)

17. M. de Gosson, The symplectic camel and phase space quantization. J. Phys.A:Math. Gen. 34(47) (2001)

16. B. Dragovich, M. de Gosson, A. Khrennikov, Some p-adic differential equations. In "p-adic functional analysis". Lecture Notes in Pure and Appl. Math. 222 Marcel Dekker (2001)

15. M. de Gosson, Lagrangian path intersections and the Leray index. Aarhus Geometry and Topology Conference. Contemp. Math., Amer. Math. Soc. 258 (2000)

14. M. de Gosson, The classical and quantum evolution of Lagrangian half-forms. Ann. Inst. Henri Poincaré 70(6) (1999)

13. M. de Gosson, The quantum motion of half-densities and the derivation of Schrödinger's equation. J. Phys. A:Math. Gen. 31(2) (1998)

12. M. de Gosson, On half-form quantization of Lagrangian manifolds and quantum mechanics in phase space. Bull. Sci. Math. 121(4) (1997)

11. M. de Gosson, On the Leray--Maslov quantization of Lagrangian submanifolds. J. Geom. Phys. 13(2) (1994)

10. M. de Gosson, The structure of q-symplectic geometry, J. Math. Pures Appl. 71(5) (1992)

09. M. de Gosson, Cocycles de Demazure--Kashiwara et géométrie métaplectique. J. Geom. Phys. 9(3) (1992)

08. M. de Gosson, Maslov indices on the metaplectic group Mp(n). Ann. Inst. Fourier 40(3) (1990)

07. M. de Gosson, La définition de l'indice de Maslov sans hypothèse de transversalité. C.R. Acad. Sci., Paris, Série I, Math. 310(5) (1990)

06. M. de Gosson, La relation entre Sp_{∞}(n) le revêtement universel du groupe symplectique Sp(n), et Sp(n)×Z.  C.R. Acad. Sci. Paris Série I, Math. 310(5) (1990)

05. M. de Gosson, Étude de la régularité à la frontière des solutions d'une classe de problèmes elliptiques singuliers. C.R. Acad. Sci., Paris, Série I, Math. 310(7) (1985)

04. M. de Gosson, Microlocal regularity at the boundary for pseudo-differential operators with the transmission property. Ann. Inst. Fourier (Grenoble) 32(3) (1982)

03. M. de Gosson, Paramétrix de transmission pour des opérateurs de type parabolique et application au problème de Cauchy microlocal. C.R. Acad. Sci. Paris, Série I, Math. 292(1) (1981)

02. M. de Gosson, Résultats microlocaux en hypoellipticité partielle à la frontière pour des opérateurs pseudo-différentiels de transmission. C.R. Acad. Sci. Paris, Série. A, 290(24) (1980)

01. M. de Gosson, Hypoellipticité partielle à la frontière des opérateurs pseudo-différentiels de transmission. Ann. Mat. Pura Appl. 123(4) (1980) [Ph.D. thesis]

Books and Monographs

1.M. de Gosson, Quantum Phase Space and the Symplectic Camel. World Scientific, 2019 [in preparation]
2.M. de Gosson, Emergence of the Quantum from the Classical: Mathematical Aspects of Quantum Processes. World Scientific, 2017
3.M. de Gosson, The Wigner Transform, World Scientific, series Advanced Texts in Mathematics, 2017
4.M. de Gosson, Introduction to Born--Jordan Quantization: Theory and applications. Springer--Verlag, series Fundamental Theories of Physics, 2016
5.M. de Gosson, Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Birkhäuser, Basel, 2011
6.M. de Gosson, Symplectic Geometry and Quantum Mechanics. Birkhäuser, Basel, series "Operator Theory: Advances and Applications" (subseries: "Advances in Partial Differential Equations"), Vol. 166, 2006
7.M. de Gosson, The Principles of Newtonian and Quantum Mechanics: the Need for Planck's Constant h; with a foreword by B. Hiley. Imperial College Press, 2001; Second edition (revised and augmented), 2016 [Best seller series]
8.M. de Gosson, Maslov Classes, Metaplectic Representation and Lagrangian Quantization. Mathematical Research Vol. 95, Wiley VCH 1997.

Edited Volumes

1.Landscapes of Time-Frequency Analysis, eds. Boggiatto, Paolo, Elena Cordero, Maurice de Gosson, Hans G. Feichtinger, Fabio Nicola, Alessandro Oliaro, and Anita Tabacco. Springer Nature, Jan. 2018
2.Proceedings of the Karlskrona Conference in the Honor of Jean Leray, Springer Verlag (2003), ca 580 pages. Ed. Maurice de Gosson
3.Maurice de Gosson, La Radio Facile (1957, Série du Faon); Reedited 2002, Éditions de la Charlynou, Karlskrona.


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