Showing papers on "Explicit symmetry breaking published in 1974"

Symmetry Behavior at Finite Temperature

Abstract: Spontaneous symmetry breaking at finite temperature is studied. We show that for the class of theories discussed, symmetry is restored above a critical temperature ${{\ensuremath{\beta}}_{c}}^{\ensuremath{-}1}$. We determine ${\ensuremath{\beta}}_{c}$ by a functional-diagrammatic evaluation of the effective potential and the effective mass. A formula for ${\ensuremath{\beta}}_{c}$ is obtained in terms of the renormalized parameters of the theory. By examining a large subset of graphs, we show that the formula is accurate for weak coupling. An approximate gap equation is derived whose solutions describe the theory near the critical point. For gauge theories, special attention is given to ensure gauge invariance of physical quantities. When symmetry is violated dynamically, it is argued that no critical point exists.

Spontaneous Symmetry Breaking in the O(N) Model for Large N

Abstract: We study the O(N) generalization of the σ model in the limit of large N, for four, three, two, and one space-time dimensions. We compute the effective potential and some momentum-dependent Green's functions. In one and two dimensions, spontaneous symmetry breakdown is impossible; any asymmetric minimum inserted in the tree-approximation potential is immediately filled in by the effects of radiative corrections. This is in agreement with general theorems. In four dimensions, the model is inconsistent; it possesses a tachyon. In three dimensions, the model seems to be consistent, and offers an interesting example of some nonlinear effects associated with spontaneous symmetry breakdown that are not present in the usual (tree-approximation) models.

Applications of Chiral Perturbation Theory: Mass Formulas and the Decay eta --> 3 pi

Abstract: Several new results on the breaking of chiral SU(3) × SU(3) are presented within the theoretical framework of chiral perturbation theory. (a) The leading-order corrections to the Gell-Mann-Okubo formula for the baryon octet are shown to be of order e32, where e is a chiral symmetry breaking parameter. An explicit exact expression is given for the leading-order corrections, which provides a new development in understanding why this formula works so well. Similarly the corrections to the Gell-Mann-Okubo formula for the ground-state pseudoscalar octet are shown to be of order e2lne (including η−η′ mixing). On the basis of these exact results it is argued that SU(3) × SU(3) symmetry is as good as SU(3) symmetry ∼30% except when one considers electromagnetic interactions. (b) We examine the η→3π decay on the assumption that it is regulated by a nonelectromagnetic isospinviolating term of the type e3u3 with u3 a member of 3¯3⊕33¯. The strength e3 of this term is related to the experimental rate including all leading-order chiral-symmetry corrections. This estimate of e3 leads to ΔI=1 hadron level shifts about a factor of 2 or 3 too large, although our estimate of e3 depends sensitively on the experimental details. (c) Octet enhancement, an exact formalism to describe η−η′ mixing, and other topics are discussed.

The normal modes of non-linear symmetric systems by group representation theory

Abstract: Group representation theory is applied to analyze a symmetric spring mass system of finite degree of freedom for non-linear normal modes of vibration. A set of symmetry operations constituting a group characterises the symmetry of a system. The symmetry adapted basis vectors, corresponding to the irreducible representations present in the reducible representation, are determined. The equations of motion in the symmetry adapted coordinates have a lower order of coupling. An equipotential surface in each invariant subspace is determined from which the normal mode vectors are evaluated in terms of the symmetry adapted basis vectors.

Self-Consistent Quantum Field Theory and Symmetry Breaking

Abstract: This lecture consists of two parts. In part I, we present a study of spontaneously broken symmetries in the terminology of quantum field theory. Though many of our results in this part help our physical and intuitive understanding of subjects and are also useful for practical computations, some of them are derived by means of certain approximations. A rigorous derivation of these results are presented in part II in which use was made of the path-integral method. The latter method is very useful for formal analysis of problems of broken symmetries.

Phenomena of multiplicity, stability, and symmetry

Abstract: The interaction of diffusion and chemical reaction plays an important role in many fundamental biological problems from the uptake of oxygen into tissues’ and the study of and activated transport to morphogenesis5j6 and the propagation of desirable genes.? The recent interest in insolubilized enzymes has opened up a new range of problems with the inclusion of electrostatic effects. The development of its mathematical theory has benefited alike from physiologists and physicists, from physical chemist and chemical engineer, and, as is often the case, there has been some unnecessary duplication through the mutual ignorance by one worker of another’s field.8 Thus the work of Roughton‘ and Hill in the late 20s and early 30s was overlooked by the chemical engineers in the late 30s and early 40s, and all parties were ignorant of the basic solutionQ developed in 1909 by a physicist, Ferencz Juttner of Breslau. Later on, Roughton’s observations on the insensitivity to shape of the effective uptake of oxygenlo reflected results that had been in the chemical engineering literature a year or two before.” This, of course, is no new phenomenon, and one of the chief benefits of a conference such as the one on which this annal is based is to familiarize each with the interests of the others.

K t3 decay and chiral-symmetry breaking

Abstract: All equal-time commutators involving axial charges and divergences which follow in the gluon quark model are abstracted without using equations of motion for the quark fields and are applied to K/sub 13/ decay. The phenomenological indications concerning the nature of chiral-symmetry breaking, which can be inferred from the existing data, are discussed with particular attention to the size of the photon and lambda quark masses as the represnetatives of the symmetry- breaking parameters. (LBS)

Views on broken symmetry

Abstract: The problem of determining the possible degrees of freedom in choosing a gauge model and connections with the old work on current algebra and symmetry breakdown is considered. Included are natural approximate symmetries of the strong interactions, second-order symmetry breaking, and weak corrections of order ..cap alpha... 16 references. (JFP)