Supersymmetry breaking in quaternion space

Keeping in view the advantages of quaternion, an attempt is made to explain supersymmetry breaking in the interacting field in terms of quaternion superpartner Hamiltonian. A complete theory for supersymmetry breaking in the thermal field in terms of bosonic and fermionic operators has been obtained along with certain restrictions due to the non-commutativity of quaternions that can hint at some hidden results. Witten index in terms of quaternion units has been obtained, and we find that energy is different along different axes. It has been observed that supersymmetry remains good symmetry at zero temperature but breaks down with temperature.