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The Dirac formalism allowing to deal with systems subject to constrains is applied to find the commutation relations that should be imposed on the canonical variables of the effective two-dimensional field theory of massless fields obtained by defining the recently introduced Bagger–Lambert– Gustavsson (BLG) three-dimensional theory of a membrane system on the compactified R × Sspace. The obtained set of constrains is of second class in the Dirac classification and should, therefore, be quantized through the introduction of the Dirac brackets which we write down in the explicit form.

Bagger–Lambert–Gustavsson Membrane Model as a Constrained System and Dirac Quantization