Non supersymmetric femion boson symmetry

In this work we present symmetry transformations relating bosons to fermions which cannot be represented as a supersymmetric algebra. We present a symmetry transformation relating a complex scalar and a fermion in four dimensions and construct a theory defined by an action that respects the symmetry quantum mechanically. We next invoke gauge symmetry by adding a gauge field and a corresponding fermion and construct two different symmetry transformations with corresponding actions such that the corresponding theories respect the fermion boson symmetry transformations quantum mechanically. Unlike in a supersymmetric theory, the vacuum energy in the above theories could be negative. Phenomenological implications of the theories are open to research.