Confrontation of Supersymmetry in Elementary Particles and Nuclear Physics

At first, I am very pleased to express my sincere gratitude to Professor Bruno Gruber and all of the people whom we owe the organisation of such a nice, not only from scientific point of view, Symposium. My second remark concerns the motivation of the present work. I am involved since several years in supersymmetries in nuclear physics and during seminars I delivered on our supersymmetry results I have got very often questions from elementary particle physicists: what is the difference between supersymmetry in elementary particle and nuclear physics; whether the Poincaré group is involved in nuclear supersymmetries; is there Clifford Algebra applied to fix the content of supermultiplets; and so on. Hence, I have been forced to l000k more carefully on the elementary particle supersymmetry from the point of view of similarities and differences with nuclear physics. I have been astonished as a new-comer how beauty and dramatic history of the elementary particle supersymmetry is and how many turning points in a supersymmetry development and application have been met. Hence, I would like to pass to you my astonishment connected with several steps in the historical evolution of elementary particle supersymmetries. Then, in the same way I will present the supersymmetry problem in nuclear physics. I will also illustrate the nuclear supersymmetry by examples of our recent results in light nuclei. In the final part I will compare both supersymmetries from mathematical and physical point of view.