THE DIRAC-NAMBU-GOTO P-BRANES AS PARTICULAR SOLUTIONS TO A GENERALIZED, UNCONSTRAINED THEORY

The theory of the usual, constrained p-branes is embedded into a large r theory in which there are no constraints. In the latter theory the F ock-Schwinger proper time formalism is extended from point-particles t o membranes of arbitrary dimension. For this purpose the tensor calcul us in the infinite-dimensional membrane space M is developed and an ac tion which is covariant under reparametrizations in M is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quan tization appears to be straightforward and elegant. No problem with un itarity arises. The conventional p-brane states are particular station ary solutions to the functional Schrodinger equation which describes t he evolution of a membrane's state with respect to the invariant evolu tion parameter tau. A tau-dependent solution which corresponds to the wave packet of a null p-brane is found. It is also shown that states o f a lower-dimensional membrane can be considered as particular states of a higher-dimensional membrane.