Collective coordinates in Fermi systems

Sunarić, S. M.

Viktor Mikhaĭlovich Galit︠s︡kiĭ

Daniel R. Bes, Jorge Kurchan B

Sam F Edwards

The collective approach to a Fermi gas is discussed by considering the wave functions of non-interacting Fermi gases in one and three dimensions, and of the interacting Fermi gas. It is shown how to write the one-dimensional case exactly in terms of collective coordinates, and how these have a well defined existence for long wavelengths even without interaction. This is extended as far as possible to three dimensions, and it is shown how the statistics affect the collective motion in the presence of interaction. A brief discussion is given of how calculations may be performed when redundant sets of coordinates are used.

Seiya Nishiyama, João da Providência

Introducing collective variables, a collective description of nuclear surface oscillations has been developed with the first-quantized language, contrary to the second-quantized one in Sunakawa's approach for a Bose system. It overcomes difficulties remaining in the traditional theories of nuclear collective motions: Collective momenta are not exact canonically conjugate to collective coordinates and are not independent. On the contrary to such a description, Tomonaga first gave the basic idea to approach elementary excitations in a one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is also expected to work well for such a problem. In this paper, on the isospin space, we define a density operator and further following Tomonaga, introduce a collective momentum. We propose an exact canonically momenta approach to a one-dimensional neutron–proton (N–P) system under the use of the Grassmann variables.

Salvador Miracle-Solé, Derek W. Robinson