| It is believed that the parafermi field theory can be used to explain some interesting features of new phenomena in astrophysics/cosmology and in new discoveries in elementary particle physics. Paragrassmann algebra, a generalization of the normal Grassmann algebra, is studied algebraically and later used to define an arbitrary p parafermi coherent state. The p=2 and p=3 cases are studied together with their self contained relations for the paragrassmann variables and the creation and annihilation operators. Two coherent states are found for both cases. We also obtain the resolution of unity for our new found p=2 Parafermi Coherent State(PCS), using the special nature of parafermi operators, i.e. that they are bounded . The eigenstate(s) of the annihilation operator for the p=1, thenormal fermion case is found to be unique but for the p=2 and p=3 para cases are found not to be unique. |
