We derive covariant, reparametrization invariant, hydrodynamical equations for a fluctuating fluid membrane, which describe both tangent-plane motion and shape-changing normal motion. We calculate the renormalization of parameters of a Rouse model in which there is a friction force proportional to the local membrane velocity. Our calculations include both the Fadeev-Popov determinant and a Liouville-like factor needed to ensure rotational invariance.
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Cai et al. (1994) studied this question.
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