We report on the recent results revealing the presence of geometric
invariants in all the phenomena in which vacuum condensates appear and we show
that Aharonov--Anandan phase can be used to provide the evidence of phenomena
like Hawking and Unruh effects and to test some behavior of quantum field
theory in curved space. A very precise quantum thermometer can be also built by
using geometric invariants.Comment: 7 pags. arXiv admin note: substantial text overlap with
arXiv:1311.289