Bosonic string-scalar model

Abstract

There are three equivalent forms of action for a string in the bosonic string theory: a first-order form (Hamiltonian formalism), a second-order form (Polyakov action), and a nonlinear form (Nambu-Goto action). All three forms of action have reparametrization symmetry, which generates the Virasoro algebra. Polyakov action resembles the action of scalar fields interacting with an external two-dimensional gravitational field. At the classical level, the Polyakov and NambuGoto actions are completely equivalent. In this paper we considered the boson string-scalar model and determined the form of action for this model. The action form for the string-scalar model was considered first in terms of the Nambu-Goto formalism. To find the energy-momentum tensor, we wrote an action in the form of a second-order formalism (Polyakov’s action). We obtained the equations of motion of the string and the constraint conditions for the considered actions. We made sure that the constraint conditions for the string remain unchanged.