Quantização de uma teoria de cordas bosônica relativística

Abstract

In this work, a relativistic theory for open and closed strings is constructed based on the lagrangian formalism for relativistic free particles, in which the action is proportional to the particle's world-line. The invariance under reparametrization of the obtained action, known as Nambu-Goto action, allows the imposition of the so called light-cone gauge, in which the famous light-cone coordinates are used, making it easy for the quantization procedure. In this gauge, the string is described by the transverse coordinates, a constant of integration and a conserved component of its momentum. This description allows one to obtain a quadratic action on these transverse coordinates that imply the same boundary conditions and equation of motion, facilitating the quantization procedure. The commutation relations between the expansion modes of the general solution for the transverse coordinates allows a interpretation in terms of creation an annihilation operators, forcing the quantized Virasoro zero mode to be ordered. Also, it is observed that the Lorentz invariance of the theory fixes the space-time dimension with $D=26$ and shifts the expression for the masses of the various particle states. At last, a similar procedure of covariant quantization is presented emphasizing the need of some constraints for physical consistency of the theory.