Casimir pistons with generalized boundary conditions: a step forward

In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type I × 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 configuratio...

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Bibliographic Details
Published in:Analysis and mathematical physics Vol. 11; no. 2
Main Authors: Fucci, Guglielmo, Kirsten, Klaus, Muñoz-Castañeda, Jose M.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Subjects:
Analysis
Boundary conditions
Manifolds (mathematics)
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Pistons
Quantum theory
Riemann manifold
Scalars
Yang-Mills theory
functions: analytic theory (11M36)
Quantum field theory on curved space backgrounds (81T20)
Zeta and
Scattering theory (81U99)
Parameter dependent boundary value problems (34B08)
Boundary value problems for second-order elliptic equations (35J25)
Symmetric and self-adjoint operators (47B25)
Quantum Theory (81S99)
Casimir effect (81T55)
General theory of linear operators (47A10)
ISSN:1664-2368, 1664-235X
Online Access:Get full text
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Summary:In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type I × 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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ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-021-00507-2