Null SuperP-Branes Quantum Theory in 4-Dimensional Space-Time

Abstract

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.

On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

“…An analogous theorem takes place in the operator BRST-BFV quantization scheme [26]. Further analysis of this problem for systems possessing the reparametrization invariance showed that the result of path integration does not depend on the choice of the gauge fermion if only appropriate gauge conditions are compatible with the boundary conditions for the parameters of the corresponding gauge transformations [24,25,26,32,13]. In particular, it was shown that the so-called "canonical gauge", when the worldline gauge field of the reparametrization symmetry of the bosonic particle is fixed to be a constant, is not admissible in this sense.…”

“…In particular, it was shown that the so-called "canonical gauge", when the worldline gauge field of the reparametrization symmetry of the bosonic particle is fixed to be a constant, is not admissible in this sense. (see [25,13] for details). Anyway one can use the canonical gauge as a consistent limit of an admissible gauge [26].…”

“…The covariant quantization of the bosonic particle has been under intensive study with both the operator and path-integral method [2,23,24,25,26,7,12,13]. In the twistorlike approach the bosonic particle has been mainly quantized by use of the operator formalism.…”

N = 2 Supersymmetric Yang–Mills Theory and the Superparticle: Twistor Transform and κ-Symmetry

“…For detailed discussion see [18]- [20]. Expression (7) does not enter the counterpart of δθ +j I : δθ …”

“…In the original formulation this symmetry is infinitely reducible and the way to remedy this drawback is to introduce auxiliary Lorentz-harmonic variables [13], [14], [15], [16], [17], [18], [19], [20] that generalize those harmonic variables advanced in [21] to describe theories with extended supersymmetry in superspace. Lorentz harmonic approach is in fact the component version of the more general superembedding approach (for review see e.g.…”