A Collective Description of Electron Interactions. I. Magnetic Interactions

David Bohm and David Pines
Phys. Rev. 82, 625 – Published 1 June 1951
PDFExport Citation

Abstract

A new approach to the treatment of the interactions in a collection of electrons is developed, which we call the collective description. The collective description is based on the organized behavior produced by the interactions in an electron gas of high density; this organized behavior results in oscillations of the system as a whole, the so-called "plasma oscillations." The collective description, in contrast to the usual individual particle description, describes in a natural way the long-range correlations in electron positions brought about by their mutual interaction. In this paper we confine our attention to the magnetic interactions between the electrons; the coulomb interactions will be discussed in a subsequent paper.

The transition from the usual single-particle description to the collective description of the electron motion in terms of organized oscillations is obtained by a suitable canonical transformation. The complete hamiltonian for a collection of charges interacting with the transverse electromagnetic field is re-expressed as a sum of three terms. One involves the collective field coordinates and expresses the degree of excitation of organized oscillations. The others represent the kinetic energy of the electrons and the residual particle interaction, which is not describable in terms of the organized oscillations, and corresponds to a screened interparticle force of short range.

Both a classical and a quantum-mechanical treatment are given, and the criteria for the validity of the collective description are discussed.

  • Received 4 December 1950

DOI:https://doi.org/10.1103/PhysRev.82.625

©1951 American Physical Society

Authors & Affiliations

David Bohm and David Pines*

  • Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

  • *Now at Randal Morgan Laboratory of Physics, University of Pennsylvania, Philadelphia, Pennsylvania.

References (Subscription Required)

Click to Expand
Issue

Vol. 82, Iss. 5 — June 1951

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Journals Archive

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×