The reduced covariant phase space quantization of the three dimensional Nambu-Goto string

TL;DR

This paper develops a covariant phase space quantization method for the 3D Euclidean Nambu-Goto string, resulting in a 2D quantum field theory with particle states of integer spin and arbitrary mass.

Contribution

It introduces a novel approach linking minimal surface representations to phase space quantization, providing explicit symplectic structure and quantization procedure for the string.

Findings

Explicit symplectic structure computed via Enneper-Weierstrass map

Quantization yields a target-space Euclidean-invariant 2D quantum field theory

Physical states correspond to particles with integer spin and arbitrary mass

Abstract

The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three translational zero modes. The symplectic structure induced trough the Enneper-Weierstrass map can be explicitly computed. Quantization is then straightforward, yielding as a result a target-space Euclidean-invariant, positive-definite, two-dimensional quantum field theory. The physical states are shown to correspond with particles states of integer spin and arbitrary mass.