Canonical Formulation of Superstring

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Abstract
The covariant action of superstring recently discovered by Green and Schwarz is studied in the canonical formalism for the constrained Hamiltonian dynamics by Dirac. There appear both the first and the second class constraints. The former generate the local supersymmetry transformations and satisfy the closed graded algebra. The latter are used to eliminate the redundant variables by defining the Dirac Bracket. By distinguishing these classes of constraints the singular property of the fermionic variables can be avoided. Although the classical Dirac bracket is well defined, there remain some difficulties for the covariant quantization in the conformal gauge. In the light cone gauge all the constraints turn out to belong to the second class and Dirac’s prescription reproduces the result of the light cone formulation of superstring developed by Green and Schwarz.

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