Field Theory of Yang-Mills Quantum Mechanics for D Particles

TL;DR

This paper introduces a novel field-theoretic framework for non-relativistic D-particle quantum mechanics within U(N) Yang-Mills theories, unifying different N values in a single Fock space and revealing new symmetries.

Contribution

It develops a new algebraic and projective formalism for D-particle fields, interpreting gauge invariance as a quantum-statistical symmetry, and connects to string dualities.

Findings

D-particle field operators change N by creating or annihilating particles.

Gauge invariance is reinterpreted as a quantum-statistical symmetry.

The formalism relates to open-closed string duality and string theory dual viewpoints.

Abstract

We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles in a Fock space of U(N) Yang-Mills theories with all different N in a unified way. D-particle field operators, creating and annihilating a D particle and hence changing N one by one, are defined. The base space of these D-particle fields is a (complex) vector space of infinite dimensions. The gauge invariance of Yang-Mills quantum mechanics is reinterpreted as a quantum-statistical symmetry, which is taken into account by setting up a novel algebraic and projective structure in the formalism. Ordinary physical observables of Yang-Mills theory, obeying the standard algebra, are expressed as bilinear forms of the D-particle fields. Together with the open-closed string duality, our new formulation suggests a trinity of three different but mutually dual viewpoints in string theory.