Null Super P ‐Branes Quantum Theory in 4‐Dimensional Space‐Time

A twistor‐like harmonic formulation of the theory of extended supersymmetrical null objects is suggested. A new harmonic form of the action for null super string and null supermembrane with N ‐extended global SUSY in 4‐dimensional space‐time is built. A way for a covariant quantization of null super p ‐branes is suggested. This way unifies the harmonic approach and the BRST‐BFV quantization method modified by the idea of the conversion of the second class constraints into the effective first class ones. The absence of anomalies and the quantum selfconsistency of null super p ‐branes, including null super membranes ( p = 2), null superstrings ( p = 1) and massless superparticle ( p = 0) in 4‐dimensional space‐time are proved. For the completeness the BRST‐BFV quantization of null p ‐brane is discussed too. The BRST‐BFV quantization method is described in details using the simple example of massless particle theory. The description of a massless particle with arbitrary spin using the Lorentz‐harmonic variables is suggested.