Relativisticp-branes without constraints and their relation to the wiggly extended objects

The invariant evolution parameter is often used in the formulation of a so-called unconstrained relativistic quantum theoryof a point particle. Such a theory is very elegant, and contains the usual Klein-Gordon or the Dirac particle as a special case. In the present paper we extend the unconstrained theory to describe a continuous set of point particles forming a string or, in general, a membrane of arbitrary dimension p.The action of this system is not invariant with respect to reparametrizations of the evolution parameter and therefore there is no constraints among the dynamical variables, and no need for ghosts in the quantized theory. Then we show that such an unconstrained membrane is equivalent to a wiggly membranewhich has variable tension on its (p+1)-dimensional worldsheet. The equations of motion admit the usual well-known Dirac-Nambu-Goto membranes as particular solutions.On leave from J. Stefan Institute, University of Ljubljana, 61111 Ljubljana, Slovenia.