Diagrammatic techniques in the martin-schwinger-puff many-body theory

James H. Crichton, Simon S. Yu

R. Cenni, F. Conte, A. Cornacchia +1 more

Daniel S. Koltun, L. Wilets

The many-body problem for nuclear matter is considered under the constraint that the density of the system vary periodically in space; this is equivalent to the problem of an external periodic potential. The method of Martin, Schwinger, and Puff is employed to derive, through second order in the amplitude of the density ripple, a set of tractable equations for the energy of the system. No new approximations are needed beyond those already assumed for the uniform density case. The model exhibits some interesting complications of the finite nuclear problem, and yet possesses sufficient simplicity for solubility. In the long-wavelength limit, an expression obtains for the explicit dependence of the energy on the density gradient; this relationship is useful in a study of the nuclear surface problem. Numerical calculations are planned.

Nicolaas P. Landsman

By use of general principles (Kubo-Martin-Schwinger condition, breakdown of Lorentz invariance, triviality arguments), the nature of diagrammatic perturbation theory in relativistic field theory at nonzero temperature is investigated. By operator-algebraic techniques it is found that the conventional method is inconsistent, and an essentially unique alternative is given.

A.S. Reiner

Using the Green's-function technique of Martin, Schwinger, and Puff, a calculation is made of the total linear response of nuclear matter, as measurable, for instance, in an inelastic electron or muon scattering experiment. In the independent-pair approximation used, two contributions stand out: the quasielastic response of properly dressed particles with well-defined lifetimes, and the contribution due to the scattering between those particles. An extensive analysis is made of the importance of the transverse component of the electromagnetic interaction as well as of the two mentioned contributions. The properly defined quasielastic scattering is predicted to dominate the scattering. A comparison is made with previous calculations by Czy\ifmmode \dot{z}\else \.{z}\fi{} and Gottfried.