December 5, 2022 Aula Seminario VI Piano, Politecnico di Milano Edificio 14 (Nave), Campus Leonardo
SPEAKER: Davide Fermi (Politecnico di Milano)
Vacuum fluctuations with zero-range potentials
The Casimir effect is a manifestation of van der Waals polarization forces
acting between atoms and molecules, in a regime where relativistic retardation
effects cannot be neglected. An effective description can be given in terms of
quantum fields influenced by classical objects, such as boundaries or external
potentials. This leads to the emergence of ultraviolet divergences which can be
treated by means of the so-called zeta-function regularization. In this seminar
I first present a rigorous implementation of the zeta-function technique, using
the language of canonical quantization for a scalar field. To this purpose,
complex powers of the elliptic operator describing the dynamics are used to
define smeared versions of the Wightman field and renormalization of
expectation values is ultimately attained by analytic continuation. Next, I
address the issue of boundary anomalies, discussing some explicitly solvable
models with zero-range potentials modeling semi-transparent walls.
Based on joint works with Livio Pizzocchero (University of Milano)
