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

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