An ambiguity exists in the prescription for deriving $n$-body potentials ($n\ensuremath{\ge}4$) from the $S$ matrix in quantum field theory. The prescription can be modified in such a way that the potentials coincide with the classical potentials.

The equations of motion of a test particle moving near the center of a massive rotating ring are derived up to the post-post-Newtonian order of approximation, by using the metric tensor for many body system which is Minkowskian at spatial infinity. Logarithmic divergences due to self-interaction of the ring appear in the equations of motion. These divergences can be removed by the procedure which is similar to the renormalization method in particle physics. In the equations of motion there appears a force directing to the rotation axis and depending on the angular velocity of the ring. This force vanishes when the magnitude of the gravitational constant times the mass of the ring divided by the radius of the ring is about one tenth of the square of the velocity of light. Under this condition it is shown that the relative magnitude of the Coriolis force to the centrifugal force in the equations of motion agrees with the expected one from the equations of motion in a rotating reference frame.

The relations sigma ( pi /sup -,p) > sigma ( pi /sup +/,p), sigma (K/ sup -,p) > sigma (K/sup + ,P), and sigma (p(with bar on top),p) > sigma (p,p) up to 20 Bev are considered under a hypot hesis on generalized isospin independence. This states that the isospin of the LAMBDA particle is zero; all hyperons have strangeness of the samc sign; thc strangeness of all hyperons is negative; and the pi and K mesons have baryon number zero. Othcr reIations may bc considered under these conditions. (L.N.N.)

16:010900Total pi /sup plus or minus /-p cross sections at 10 to 20 Bev were measured using previous techniques (NSA, 15: 29935; 31307). Data are presented in graphical and tabular forms. Agreement with theory was obtained. (L.N.N.)

: IN THE SCATTERING OF VERY HIGH-ENERGY PROTONS FROM THE NUCLEONS WITHIN TARGET NUCLEI, IT IS FOUND THAT THE SCATTERED PROTONS HAVE A DISTRIBUTION OF ENERGIES. These experiments where performed which show a sharp peak in the energy distribution which corresponds to elastic scattering of the incident protons, and also a broader peak at somewhat lower energy which corresponds to nearly elastic scattering of the incident protons. An explanation of this latter quasi-elastic peak is offered in terms of the diffraction scattering of one of the pions in the cloud of the target nucleon. This diffraction scattering of the pion by the incident nucleon results in a moderate energy loss of the nucleon, so that it emerges in the quasi-elastic peak. (Author)

The recent high-energy electron-proton scattering experiments at Stanford are analysed in connection with the small mass difference of the nucleon. If nucleons are rigid bodies, then it is shown that a consistent interpretation is given when we ascribe to the electron a finite size of the same order as those of nucleons. Discussions of this result are extended to other related phenomena.

Starting from several physically reasonable assumptions, taken byKällén andLehmann, various Green’s functions are transformed into the parametrical integral form with spectral functions. Then a method is presented to convert the equations connecting various Greens’ functions into those among the corresponding spectral functions alone.