• Abhijit Banerjee
• Partha Mandal

We have demonstrated a simple theoretical model, involving the pseudo bosons within the second derivative supersymmetric (SSUSY) framework, which under certain suitable constraint produces a triplet of super partner Hamiltonians, that depict polynomial supersymmetry (PSUSY) for pseudo bosonic systems. A class of non singular oscillators have found, as a pseudo bosonic system using SSUSY and PSUSY representations of our choice. From the zero mode states of their corresponding quasi Hamiltonian, we have calculated the Witten index that reveals, the underlying supersymmetry (SUSY) is unbroken in nature.

Supersymmetry, Pseudo boson, SSUSY, PSUSY.

"An Unbroken Pseudo-Bosonic System Under the Second Derivative and Polynomial Super Symmetry", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 6, page no.220-225, June-2018, Available :http://www.jetir.org/papers/JETIR1806153.pdf

"An Unbroken Pseudo-Bosonic System Under the Second Derivative and Polynomial Super Symmetry", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 6, page no. pp220-225, June-2018, Available at : http://www.jetir.org/papers/JETIR1806153.pdf