Casimir-like corrections to the classical tensions of the strings and membranes

We find the Casimir-like energies for strings and membranes. We show that the related Casimir forces can be interpreted as quantum corrections to the classical tensions of the strings and membranes. We see that these corrections always increase the tensions of the circular string as well as spherical membrane, while for the straight string, rectangular and cylindrical membranes, these Casimir forces may increase or decrease the tensions. So we find that the quantum vacuum can break the (tensional) isotropy of the rectangular and cylindrical membranes. Also obtaining the nonzero-temperature Casimir energy, we find relations for the tensions at nonzero temperature.