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Symplectic Covariance Properties

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Book cover Born-Jordan Quantization

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 182))

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Abstract

Given an operator \(\widehat{A}=\mathrm{{Op}}(a)\) a natural question that arises is what happens to that operator when one makes a change of variables in the symbol a.

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References

  1. G.B. Folland, Harmonic Analysis in Phase Space (Princeton University Press, Princeton, 1989). Annals of Mathematics Studies

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  2. M. de Gosson, Symplectic Geometry and Quantum Mechanics (Birkhäuser, Basel, 2006)

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  3. M. de Gosson, Metaplectic representation, Conley–Zehnder index, and Weyl calculus on phase space. Rev. Math. Phys. 19(8), 1149–1188 (2007)

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  4. M. de Gosson, On the usefulness of an index due to Leray forstudying the intersections of Lagrangian and symplectic paths. J. Math. Pures Appl. 91, 598–613 (2009)

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  5. M. de Gosson, Symplectic Methods in Harmonic Analysis (Applications to Mathematical Physics, Birkhäuser, 2011)

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  6. M. de Gosson, Symplectic covariance properties for Shubin and Born–Jordan pseudo-differential operators. Trans. Am. Math. Soc. 365, (2013)

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  7. K. Gröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, Boston, 2000)

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  8. J. Leray, Lagrangian Analysis and Quantum Mechanics, Amathematical Structure Related to Asymptotic Expansions and the Maslov Index (The MIT Press, Cambridge, 1981); translated from AnalyseLagrangienne RCP 25, Strasbourg Collège de France, 1976–1977

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  9. E.M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals (Princeton University Press, 1993)

    Google Scholar 

  10. M.W. Wong, Weyl Transforms (Springer, 1998)

    Google Scholar 

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Correspondence to Maurice A. de Gosson .

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de Gosson, M.A. (2016). Symplectic Covariance Properties. In: Born-Jordan Quantization. Fundamental Theories of Physics, vol 182. Springer, Cham. https://doi.org/10.1007/978-3-319-27902-2_13

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