Effective Hamiltonians for strings and their spatial symmetry

The effective Hamiltonian governing the fluctuations of a (d-n)-dimensional string into the remaining n dimensions in a d bulk dimensional system is derived using semiclassical methods in the long-distance limit and found to represent the hypersurface area of the string. The author also derives the effective Hamiltonian for strings with an associated O(2) Goldstone mode, and obtains a field theory defined on a curved surface given by the interface's position. The role of spatial symmetries in determining the form of the effective Hamiltonian is illustrated.