Quantum mechanics of a superparticle with 1/4 supersymmetry breaking

We study quantum mechanics of a massive superparticle in d=4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N=8→N=2. Its worldline action contains a Wess-Zumino term, explicitly breaks d=4 Lorentz symmetry and exhibits one complex fermionic K symmetry. We perform the Hamiltonian analysis of the model and quantize it in two different ways: with gauge-fixed K symmetry and in the Gupta-Bleuler formalism. Both approaches give rise to the same supermultiplet structure of the space of states. It contains three irreducible N=2 multiplets with the total number of (4+4) complex on-shell components. These states prove to be in one-to-one correspondence with the de Rham complex of p-forms on a three-dimensional subspace of the target x manifold. We analyze the vacuum structure of the model and find that the nontrivial vacua are given by the exact harmonic one- and two-forms. Despite the explicit breaking of d=4 Lorentz symmetry in the fermionic sector, the d=4 massshell condition is still valid in the model.