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The Pearcey Equation: From the Salpeter Relativistic Equation to Quasiparticles

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Nonlocal and Fractional Operators

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 26))

Abstract

This work presents the Pearcey equation, a quasi-relativistic wave equation for spinless particles with non-zero rest mass. This equation was introduced as a mathematical tool to address the problem of nonlocality concerning the pseudo-differential operator in the Hamiltonian of the Salpeter equation. The Pearcey equation can be considered as a way to relativity since it embeds the peculiar features of the relativistic evolution even if it looks very similar to the Schrödinger equation. In light of the catastrophe theory, the Pearcey equation acquires a deeper physical meaning as a candidate for describing quasiparticles.

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Acknowledgements

A.L. was supported by the Polish National Agency for Academic Exchange NAWA project: Program im. Iwanowskiej PPN/IWA/2018/1/00098 and supported by the NCN research project OPUS 12 no. UMO-2016/23/B/ST3/01714. I would like to thank the anonymous referee for giving valuable suggestions and constructive comments.

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Authors and Affiliations

  1. H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul. Eljasza-Radzikowskiego 152, 31342, Kraków, Poland

    A. Lattanzi

  2. ENEA FSN-FUSPHYS-TSM, Via E. Fermi 45, 00044, Frascati, Rome, Italy

    A. Lattanzi

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  1. A. Lattanzi
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Correspondence to A. Lattanzi .

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Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Luisa Beghin

  2. Department of Physics and Astronomy (DIFA), Università di Bologna, Bologna, Italy

    Francesco Mainardi

  3. Department of Mathematics, Università di Bari, Bari, Italy

    Roberto Garrappa

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Lattanzi, A. (2021). The Pearcey Equation: From the Salpeter Relativistic Equation to Quasiparticles. In: Beghin, L., Mainardi, F., Garrappa, R. (eds) Nonlocal and Fractional Operators. SEMA SIMAI Springer Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-69236-0_10

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