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Casimir pistons with generalized boundary conditions: a step forward

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Abstract

In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type \(I\times N\) where I is an interval of the real line and N is a smooth compact Riemannian manifold. Our analysis represents a generalization of previous results obtained for pistons configurations as we consider all possible boundary conditions that are allowed to be imposed on the scalar fields. We employ the spectral zeta function formalism in the framework of scattering theory in order to obtain an expression for the Casimir energy and the corresponding Casimir force on the piston. We provide explicit results for the Casimir force when the manifold N is a d-dimensional sphere and a disk.

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Acknowledgements

JMMC and KK are grateful to the Spanish Government-MINECO (MTM2014- 57129-C2-1-P) for the financial support received. JMMC is grateful and the Junta de Castilla y León (BU229P18, VA137G18 and VA057U16) for the financial support. JMMC would like to deeply acknowledge and honour all the support, the teaching, and the knowledge received from Professor Jose M. Muñoz-Porras during all his life: it is the greatest honour to be your son.

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Authors and Affiliations

  1. Department of Mathematics, East Carolina University, Greenville, NC, 27858, USA

    Guglielmo Fucci

  2. GCAP-CASPER Department of Mathematics, Baylor University, Waco, TX, 76798, USA

    Klaus Kirsten

  3. Mathematical Reviews, American Mathematical Society, 416 4th St., Ann Arbor, MI, 48103, USA

    Klaus Kirsten

  4. Departamento de Física Teórica, Atómica, y Óptica, Universidad de Valladolid, Valladolid, Spain

    Jose M. Muñoz-Castañeda

Authors
  1. Guglielmo Fucci
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  2. Klaus Kirsten
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  3. Jose M. Muñoz-Castañeda
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Correspondence to Jose M. Muñoz-Castañeda.

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Fucci, G., Kirsten, K. & Muñoz-Castañeda, J.M. Casimir pistons with generalized boundary conditions: a step forward. Anal.Math.Phys. 11, 70 (2021). https://doi.org/10.1007/s13324-021-00507-2

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