« Dynamical » lagrangian for the many body problem

J. K. Percus, G. J. Yevick

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A « dynamical » Lagrangian approach to the many body problem in the collective co-ordinate formulation is made possible with the aid of the two-body correlation function. As a consequence, the values of the flctitious masses and frequencies for the collective co-ordinate harmonic oscillators, which represent the physical problem, are dependent on the average motion of the system. Moreover, the introduction of the center of mass and relative co-ordinates for the q k occasions no difficulty in the present approach. In Part B of the paper, preliminary considerations are presented on the physical extent of the domain of action of q-space; various techniques are utilized to probe its structure. It is found in this way that the « diameter » of q-space is of the order of N 1/2. Application is made to the speed of sound in a fluid.

Original languageEnglish (US)
Pages (from-to)65-82
Number of pages18
JournalIl Nuovo Cimento
Issue number1
StatePublished - Jan 1957

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics


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