Nonabelian monopoles from matrices

We study the expectation value of (the product) of the one-particle project or(s) in the reduced matrix model and matrix quantum mechanics in general. This quantity is given by the nonabelian Ferry phase: we discuss the releva nce of this with regard to the spacetime structure. The case of the USp mat rix model is examined from this respect. Generalizing our previous work, we carry out the complete computation of this quantity which takes into accou nt both the nature of the degeneracy of the fermions and the presence of th e spacetime points belonging to the antisymmetric representation. We find t he singularities as those of the SU(2) Yang monopole connection as well as the pointlike singularities in 9 + 1 dimensions coming from its SU(8) gener alization. The former type of singularities, which extend to four of the di rections lying in the antisymmetric representations, may be regarded as see ds of our four-dimensional spacetime structure and is not shared by the IIB matrix model. From a mathematical viewpoint, these connections can be gene ralizable to arbitrary odd space dimensions due to the nontrivial nature of the eigenbundle and the Clifford module structure. (C) 2000 Elsevier Scien ce B.V. All rights reserved.