Hamiltonian approach and quantization of $D=3, {\cal N}=1$ supersymmetric non-Abelian multiwave system

TL;DR

This paper develops a Hamiltonian formalism and quantization method for a supersymmetric non-Abelian multiwave system in 3D, leading to a novel matrix model field theory with supersymmetry and fermionic operators.

Contribution

It introduces a new quantization approach for a 3D supersymmetric multiwave system, extending matrix model techniques to include fermionic superpartners.

Findings

Quantization yields supersymmetric matrix field equations with su(N)-valued matrices.

Fermionic superpartners are represented as abstract operators acting on the state vector.

Bosonic limit solutions confirm the consistency of the derived equations.

Abstract

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.