Classical image of many-fermion system and its canonical quantization

The TDHF theory is valid only for describing the collective and the intrinsic motions only in even-fermion system. The both types of the motions are of the particle-hole pair type. If we intend to give a classical image for odd-fermion system, the TDHF theory should be extended. For such systems, we must express the intrinsic degrees of freedom in terms of the independent-particle picture. A classical image of fermions can be given by the use of the Grassmann variables. Therefore, it becomes interesting to investigate how the TDHF theory is extended so as to describe the collective and the independent-particle motions in terms of the collective and the Grassmann variables. Main aim of this talk is to sketch a possible idea for the above-mentioned problems. The authors proved that the formulation gives a classical image of many-fermion system and the requantization becomes a boson expansion. Obeying the true spirit of the TDHF theory in the Hamilton's canonical form, the second and the third problem have been completely originated by the present authors. With the aid of the TDHF theory in the Dirac's canonical form, we can obtain equation of collective submanifold and it gives us the separation of the whole degrees of freedom into the collective and the intrinsic ones. In the third problem, the fermion coherent state constructed on the Slater determinant plays a central role. (orig./HSI)