Abstract
Unique twistor--like Lorentz harmonic formulation for all N=1 supersymmetric extended objects (super-p-branes) moving in the space--time of arbitrary dimension D (admissible for given ) are suggested. The equations of motion are derived, explicit form of the κ-symmetry transformations is presented and the classical equivalence to the standard formulation is proved. The cases with minimal world--sheet dimensions , namely of D=10 heterotic string and D=11 supermembrane, are considered in details. In particular, the explicit form of irreducible κ-symmetry transformations for D=11 supermembrane is derived.
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