  We develop Hamiltonian formalism and quantize supersymmetric non-Abelian
multiwave system (nAmW) in D=3 spacetime constructed as a simple counterpart of
11D multiple M-wave system. Its action can be obtained from massless
superparticle one by putting on its worldline 1d dimensional reduction of the
3d SYM model in such a way that the new system still possesses local fermionic
kappa-symmetry.
  The quantization results in a set of equation of supersymmetric field theory
in an unusual space with su(N)-valued matrix coordinates. Their superpartners,
the fermionic su(N)-valued matrices, cannot be split on coordinates and momenta
in a covariant manner and hence are included as abstract operators acting on
the state vector in the generic form of our D=3 Matrix model field equations.
We discuss the Clifford superfield representation for the quantum state vector
and in the simplest case of N=2 elaborate it in a bit more detail. As a check
of consistency, we show that the bosonic Matrix model field equations obtained
by quantization of the purely bosonic limit of our D=3 nAmW system have a
nontrivial solution.

High Energy Physics - Theory