The paper presents a study of non-linear electrodynamics derived from quantized strings, focusing on the effective action for an abelian vector field coupled to virtual open Bose strings. The work computes the effective action for the case of a constant field strength and D=26 space-time dimensions. The tree-level effective lagrangian is shown to coincide with the Born-Infeld lagrangian, which is given by the square root of the determinant of the metric tensor with a correction term involving the field strength. The study is carried out in both the "tree" and "one-loop" approximations, with the tree-level result matching the Born-Infeld action. The one-loop contribution is also computed, showing that the effective action includes non-polynomial terms in the curvature and field strength. The results are compared with known results in supergravity and particle theory, and the paper discusses the implications for string theory and the possibility of non-trivial vortex solutions. The study also touches on the generalization of the results to non-abelian cases and superstrings, as well as the potential for exact solutions in certain limits. The paper concludes with remarks on the significance of the Born-Infeld action in the context of string theory and the need for further investigation into the properties of the effective action.The paper presents a study of non-linear electrodynamics derived from quantized strings, focusing on the effective action for an abelian vector field coupled to virtual open Bose strings. The work computes the effective action for the case of a constant field strength and D=26 space-time dimensions. The tree-level effective lagrangian is shown to coincide with the Born-Infeld lagrangian, which is given by the square root of the determinant of the metric tensor with a correction term involving the field strength. The study is carried out in both the "tree" and "one-loop" approximations, with the tree-level result matching the Born-Infeld action. The one-loop contribution is also computed, showing that the effective action includes non-polynomial terms in the curvature and field strength. The results are compared with known results in supergravity and particle theory, and the paper discusses the implications for string theory and the possibility of non-trivial vortex solutions. The study also touches on the generalization of the results to non-abelian cases and superstrings, as well as the potential for exact solutions in certain limits. The paper concludes with remarks on the significance of the Born-Infeld action in the context of string theory and the need for further investigation into the properties of the effective action.