The ground state energy of the massive scalar field with non-conformal coupling $\xi$ on the short-throat flat-space wormhole background is calculated by using zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that the stable configuration of wormholes can exist for $\xi > 0.123$. In particular case of massive conformal scalar field with $\xi=1/6$, the radius of throat of stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has radius of throat $a\approx 0.0141 l_p $ and mass of scalar boson $m\approx 11.35 m_p$ ($l_p$ and $m_p$ are the Planck length and mass, respectively).Comment: revtex, 18 pages, 3 eps figures. accepted in Phys.Rev.

We consider the vacuum energy of the electromagnetic field interacting with a spherical plasma shell together with a model for the classical motion of the shell. We calculate the heat kernel coefficients, especially that for the TM mode, and carry out the renormalization by redefining the parameters of the classical model. It turns out that this is possible and results in a model, which in the limit of the plasma shell becoming an ideal conductor reproduces the vacuum energy found by Boyer in 1968.

We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop a general approach to finding the self-force and apply it to the two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it turns out to be an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.

We found the contribution to the vacuum expectation value of the energy-momentum tensor of a massive Dirac field due to the conical geometry of the cosmic string space-time. The heat kernel and heat kernel expansion for the squared Dirac operator in this background are also considered and the first three coefficients were found in an explicity form.