M-theory and Deformation Quantization

We discuss deformation quantization of the covariant, light-cone and conformal gauge-fixed p-brane actions (p>1) which are closely related to the structure of the classical and quantum Nambu brackets. It is known that deformation quantization of the Nambu bracket is not of the usual Moyal type. Yet the Nambu bracket can be quantized using the Zariski deformation quantization (discovered by Dito, Flato, Sternheimer and Takhtajan) which is based on factorization of polynomials in several real variables. We discuss a particular application of the Zariski deformed quantization in M-theory by considering the problem of a covariant formulation of Matrix theory. We propose that the problem of a covariant formulation of Matrix theory can be solved using the formalism of Zariski deformed quantization of the triple Nambu bracket.