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

Summary

The theory of the usual, constrainedp-branes is embedded into a larger theory in which there are no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary dimension. For this purpose the tensor calculus in the infinite-dimensional membrane space ℳ is developed and an action which is covariant under reparametrizations in ℳ is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quantization appears to be straightforward and elegant. No problem with unitarity arises. The conventionalp-brane states are particular stationary solutions to the functional Schrödinger equation which describes the evolution of a membrane’s state with respect to the invariant evolution parameterτ. A τ-dependent solution which corresponds to the wave packet of a nullp-brane is found. It is also shown that states of a lower-dimensional membrane can be considered as particular states of a higher-dimensional membrane.