Liouville-von Neumann approach and time-dependent Gaussian approximation

We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the time-dependent systems and show that many aspects of the dynamics are independent of the details of time evolution, e.g., the squeezing of the wave-function is determined by the effective potential of the final stage of time-evolution.Comment: 10 pages, 2 figure

Casimir energy of a spherical shell in κ−\kappa-Minkowski spacetime

We study the Casimir energy of a spherical shell of radius $a$ in $\kappa$-Minkowski spacetime for a complex field with an asymmetric ordering and obtain the energy up to $O(1/\kappa^2)$. We show that the vacuum breaks particle and anti-particle symmetry if one requires the spectra to be consistent with the blackbody radiation at the commutative limit.Comment: 23 pages, 3 figures, add more analysi