Scalar Casimir effect for a conducting cylinder in a Lorentz violating background

TL;DR

This paper investigates how spontaneous Lorentz symmetry breaking affects the scalar Casimir effect on a conducting cylindrical shell, revealing that Lorentz violation significantly reduces the Casimir force.

Contribution

It provides explicit Green's functions and analytical expressions for the Casimir pressure in a Lorentz-violating scalar field theory with cylindrical boundary conditions.

Findings

Casimir pressure depends strongly on Lorentz-violating coefficient

Lorentz violation tends to diminish the Casimir force

Numerical and analytical results agree with Lorentz invariant case when Lorentz violation is absent

Abstract

Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. The scalar field is modeled by a Lorentz-breaking extension of the theory for a real scalar quantum field in the bulk regions. The corresponding Green's functions satisfying Dirichlet boundary conditions on the cylindrical shell are derived explicitly. We express the Casimir pressure (i.e. the vacuum expectation value of the normal-normal component of the stress-energy tensor) as a suitable second-order differential operator acting on the corresponding Green's functions at coincident arguments. The divergences are regulated by making use of zeta function techniques, and our results are successfully compared with the Lorentz invariant case. Numerical calculations are carried out for the Casimir pressure as a function of the Lorentz-violating coefficient, and an approximate analytical expression for the force is presented as well. It turns out that the Casimir pressure strongly depends on the Lorentz-violating coefficient and it tends to diminish the force.