In theoretical physics, massive representations of an extended supersymmetry algebra called Bogomol'nyi–Prasad–Sommerfeld (BPS) states (named after Evgeny Bogomolny, M.K.
Prasad, and Charles M. Sommerfield) have mass equal to the supersymmetry central charge Z. Quantum mechanically, if the supersymmetry remains unbroken, exact equality to the modulus of Z exists.
Their importance arises as the supermultiplets shorten for generic massive representations, with stability and mass formula exact.
The generators for the odd part of the superalgebra have relations:[1] where:
Take linear combinations of the above generators as follows: Consider a state ψ which has 4 momentum