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A master action for bosonic strings and membranes, interpolating between theNambu--Goto and Polyakov formalisms, is discussed. The role of the gaugesymmetries vis-\`{a}-vis reparametrization symmetries of the various actions isanalyzed by a constrained Hamiltonian approach. This analysis reveals thedifference between strings and higher branes, which is essentially tied to adegree of freedom count. The cosmological term for membranes follows naturallyin this scheme. The conncetion of our aproach with the Arnowitt--Deser--Misnerrepresentation in general relativity is illuminated.Comment: LaTex, 23 pages; discussion on ADM representation included and new  references adde

Interpolating action for strings and membranes: A study of symmetries in the constrained Hamiltonian approach