Exact Results in Quantum Theory

I will discuss the Casimir effect in mean-field Bose gases. Afterdemonstrating how varying the dispersion influences the Casimir effectfor realistic cases, I will analyse dispersions characterised byarbitrary power-law-type low-momentum asymptotic behavior. I will showthat the Casimir amplitudes are not well defined for the general caseand the physically relevant results are recovered by cancellation ofsingular factors.