Infinite Charge Research Articles

Equivalence problems in models with infinite renormalizations

The conditions for the equivalence between two quantum field-theoretical models with infinite mass and charge renormalizations are investigated, taking into account not only observable effects, but also the details of Hilbert-space formalism. The models are of Lee-model type with relativistic kinematics, with interactions V ↔ Nθ and Nθ ↔ Nθ respectively.

Excitation of lithium-like ions by electron impacts

The cross sections corresponding to the transitions Q(2s → np) and for 2 ⩽ n ⩽ 7 have been computed for Be II, N V, and Ne VIII, using the Coulomb-Born approximation. The cross sections Q(2s → 3p) and Q(2s → 7p) have also been computed for a hydrogenic ion with an infinite nuclear charge. The results obtained are compared with the semi-classical and the g treatments. Simple analytic forms are fitted to the calculated cross sections. The corresponding parameters are then extrapolated along the quantum number n and the charge Z. Tables and graphs are given which enable one to rapidly obtain any cross sections of the type Q(2s → np) in any ion of the lithium isoelectronic series.

On Trapped Trajectories in Brownian Motion

The Brownian motion of an ion in the attractive field of an infinite line charge is investigated with reference to the existence of trapped trajectories, i.e., trajectories which never depart from the neighborhood of the center of attraction. It is shown that there is a discontinuity in the nature of the Brownian motion as a function of the line charge density, marked by the appearance of trapped trajectories when the line charge density becomes greater than a critical value.

Electrostatic Binding Energy in a Body-Centered Structure of Parallel Charge Doublet Chains

The binding energy between chains in a body-centered tetragonal structure, consisting of infinite charge doublet chains parallel to the c axis, is considered as a function of two lattice parameters. Graphs are plotted of the variation of the binding energy with these parameters. The results are applied to the particular case of metaldehyde.

On interacting spinor fields in one dimension

The physical significance of the exact solution of interacting spinor fields in one space dimension is discussed. It is argued that the absence of ghosts in this theory is connected with the fact that there is only a field hut no infinite charge renormalization.

Reactive Corrections for the Elastic Scattering of an Electron

One of the simplest problems about the reaction of radiation field on the electron is the radiative correction for the elastic scattering cross section of an electron by a fixed electrostatic potential. But attemr-ts to solve this problem have heretofore been beset by divergence difficulties. Recently, however, a certain part of the divergent corrections was found to be just cancelled if the C-meson field is introduced in addition to the radiation field. (1)(2) At the same· time it became clear that the divergences can be attributed to the self~energy and vacuum polarization; so that immediately after that subtraction or amalgamation was proposed in order to obtain a finite result. (~) Chr01zolol.;·ica1t.y, the C-meson hypothesis was thus put forward first and then the self-consistent subtraction method was presented as an alternative prescription. Blit through further considerations we have now the following opinion with regard to the logical relation of these two hypotheses: The self-consistent subtraction method analyses in what· manner the divergences occur and finds that they are reduced to unobservable renormalizatiol1 of mass and charge and that one can obtain a finite reactive correction by merely replacing the theoretical infinite mass and charge by the empirical ones. This conclusion has been indeed verified· by several experiments, bllt the fundamental difficulty of divergence remains still unsolved. The Cmeson hypothesis, on the other hand, gives a tentative solution as to the origin of one of these divergences. Thus it aims at a higher substantial stage of the theory and seems at the S:'lme time unevitably less confirmative before it obtains an experimental support. Another remark is that the