Towards field theory of multiple D0-branes. Hamiltonian mechanics and quantization of simplest 3D prototype of multiple D0-brane system

TL;DR

This paper develops the Hamiltonian mechanics and performs covariant quantization of a 3D prototype model of multiple D0-branes, aiming to deepen understanding of supersymmetric field theories related to string theory.

Contribution

It introduces the Hamiltonian formulation and covariant quantization of a simplified 3D multiple D0-brane system, advancing the study of supersymmetric matrix models.

Findings

Derived a supersymmetric system of equations in super-spacetime with matrix coordinates.

Constructed a Hamiltonian framework for the 3D D0-brane prototype.

Performed covariant quantization leading to new supersymmetric equations.

Abstract

Recently we have constructed a completely supersymmetric nonlinear action possessing the properties expected from multiple D0-brane system. Its quantization should result in an interesting supersymmetric field theory in the (super)space with additional matrix coordinates which can provide an important insights in the study of String Theory. As a first stage toward this aim, in this paper we construct the Hamiltonian mechanics and perform covariant quantization of the simplest three dimensional counterpart of the ten dimensional multiple D0-brane model. We obtain a supersymmetric system of equations in super-spacetime enlarged by bosonic and fermionic matrix coordinates which appears as a result of such quantization and discuss some of its properties.