Low-energy parabosonic membrane: new critical dimensions and deformed noncommutativity

We study a classical perturbative membrane based on the string-limit model and we discuss the consistency of the theory where the closure of the classical constraints algebra is verified. We paraquantize the model (extended string) both in the covariant and the transverse approaches. From the generalized Poincaré algebra, the so-called Poincaré (para) algebra, we show that the space-time critical dimensions D are related to the order of the paraquantization Q by the relation D = 3+24/Q. The symplectic structure is generalized for the paraquantum case and applied to the parabosonic membrane coupled to a constant 3-form field. This leads to a deformed noncommutative relations at the ends of the membrane (extended string) describing a geometry which might be called a q-noncommutativity