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The basic question raised in this paper is the relationship between group theoretical and physical notions. In particular the physical significance of the mathematical entities occurring in group‐representations is examined in detail. For this reason a brief outline is presented of the mathematical definitions and status of non‐linear realizations of groups. Special non‐linear realizations of the Lorentz and Poincare groups are exhibited. The possible physical meaning of these realizations is discussed. It is shown that there is a fundamental interpretation question involved, which indicates that the identical formalism can describe a wide variety of physical phenomena. The classical (Wigner) theory of the representations of the Poincare group, allows the description of many‐particle systems in terms of elements and operators in tensor products of Hilbert space. An appropriate adaptation of this procedure suggests that the utilization of the non‐linear realization of the Poincare group, describes a relativistic many‐particle system in interaction. General requirements such as causality are shown to be compatible with the formalism of the non‐linear realizations.

A technique for improving the rate of convergence of the solution of field problems by the method of finite differences called SER (successive extrapolated relaxation) has been developed. Sufficient saving in computing time is obtained by the method so that it is feasible to solve three‐dimensional field problems. This method uses conventional overrelaxation for every three iterations and then extrapolates simultaneously to the solution using a modification of Aitken's formula. In this paper, this method is applied to obtain the field in three dimensions from “T bar” circuits used for propagating magnetic bubbles. Symmetry considerations have been used so that the analysis is required over only one half of the propagating period. The permalloy circuit is idealized for these calculations.

At tricritical points thermodynamic functions scale with respect to three independent field variables. Such points have been called critical points of the third order. We present, in this paper, a general scaling hypothesis for such critical points and demonstrate how the concept of invariant spaces leads naturally to the prediction of data collapsing from volumes to lines in terms of “double‐power scaling functions”.