Casimir pistons with generalized boundary conditions: a step forward

Fucci, Guglielmo; Kirsten, Klaus; Muñoz-Castañeda, Jose M.

doi:10.1007/s13324-021-00507-2

Casimir pistons with generalized boundary conditions: a step forward

Guglielmo Fucci
(
- East Carolina U.
)
,
Klaus Kirsten
(
- Baylor U.
)
,
Jose M. Muñoz-Castañeda
(
- Valladolid U.
)

Jun 20, 2019

27 pages

Published in:

Anal.Math.Phys. 11 (2021) 2, 70

Published: Mar 1, 2021

e-Print:

1906.08486 [math-ph]

DOI:

10.1007/s13324-021-00507-2

View in:

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Abstract: (Springer)

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.

Note:

27 pages and 5 figures. A new section has been added. To appear in Analysis and Mathematical Physics

Quantum Theory (81S99)
Quantum field theory on curved space backgrounds (81T20)
Casimir effect (81T55)
Scattering theory (81U99)
Parameter dependent boundary value problems (34B08)
Boundary value problems for second-order elliptic equations (35J25)
Zeta and L-functions: analytic theory (11M36)
Symmetric and self-adjoint operators (47B25)
General theory of linear operators (47A10)
effect: Casimir

References(45)

Figures(5)

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