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The theory of the usual, constrained p-branes is embedded into a largertheory in which there is no constraints. In the latter theory theFock-Schwinger proper time formalism is extended from point-particles tomembranes of arbitrary dimension. For this purpose the tensor calculus in theinfinite dimensional membrane space M is developed and an action which iscovariant under reparametrizations in M is proposed. The canonical andHamiltonian formalism is elaborated in detail. The quantization appears to bestraightforward and elegant. No problem with unitarity arises. The conventionalp-brane states are particular stationary solutions to the functionalSchroedinger equation which describes the evolution of a membrane's state withrespect to the invariant evolution parameter tau. A tau-dependent solutionwhich corresponds to the wave packet of a null p-brane is found. It is alsoshown that states of a lower dimensional membrane can be considered asparticular states of a higher dimensional membrane.Comment: 28 page

The Dirac-Nambu-Gotop-branes as particular solutions to a generalized, unconstrained theory