6 problems

Let $\Omega$ be the region occupied by the quantized field, with boundary $\partial\Omega$, and let $p_i^{\mathrm{ren}}({\bf x})$ be the renormalized pressure obtained by analytic…

Periodic-boundary-condition vacuum-energy conjecture. Periodic boundary conditions select the field component of the vacuum energy, equal to $\varepsilon_f$ up to a factor; this co…

Let $D$ be the spatial dimension, and let $\hat{c}_D$ denote the coefficient described above in the high-temperature expansion of the Casimir free energy for a spherical shell, wit…

Let a sphere be deformed into a spheroid with small ellipticity $e$, and let $E(e)$ denote its zero-point energy under the relevant massless scalar boundary conditions. Boundary de…

Boundary deformation conjecture. For small ellipticity, the electromagnetic zero-point energy satisfies

Let a boundary be deformed by a small deformation that preserves its volume, and let the zero-point energy associated with the boundary be denoted by $E$. Boundary deformation conj…