Field theory of Yang-Mills quantum mechanics for D particles

We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles (D0 branes) in a Fock space of U(N) Yang-Mills theories with all different N simultaneously. D-particle field operators, which create and annihilate a D particle and hence change the value of N by one, are defined. The base space of these D-particle fields is a (complex) vector space of infinite dimension. 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 dual viewpoints of string theory. (author)