Collective Representation of the Many-Particle System Interacting through Arbitrary Two-Body Potential
Naomi Shohno
We develope a collective description of the many-particle system interacting through an arbitrary two-body potential. The description is given both in terms of the second quantized form and in terms of an auxiliary field analogous to the longitudinal electromagnetic field. As Bohm-Pines theory of the collective description has some unsatisfactory features concerning the subsidiary condition imposed on the auxiliary field, we propose here a strict method of treatment on the subsidiary condition. To obtain the useful result of the collective representation, we have to take the three steps of the canonical transformations. Though the first two transformations are the same as those of B-P, the third transformation, which is not applied by B-P and is characteristic of our theory, is necessary for obtaining a meaningful result. By using both the strict subsidiary condition and the three canonical transformations, the collective field coordinate and the particle coordinate are separated not only in the total Hamiltonian but also in the subsidiary condition. Moreover, we are able to clarify the correct meaning of the subsidiary condition and clarify also the connections between our theory and the theory of Sawada-Brueckner-Fukuda-Brout.
Progress of Theoretical Physics•Nov 1, 1960•1 citation