Showing papers on "Explicit symmetry breaking published in 1969"
TL;DR: Some well known reactions can be used to illustrate that symmetry breaking chemical instabilities may be important in biological systems.
Abstract: Some well known reactions can be used to illustrate that symmetry breaking chemical instabilities may be important in biological systems.
128 citations
TL;DR: In this paper, the symmetry properties of the system are considered and a general procedure is given for constructing a suitable space Φ out of the labeled observables of a system and the representation U describing its symmetry properties.
Abstract: The quantum‐mechanical formalism developed in a previous article and based on the use of a rigged Hilbert space Φ ⊂ H ⊂ Φ′ is here enlarged by taking into account the symmetry properties of the system. First, the compatibility of a particular symmetry with this structure is obtained by requiring Φ to be invariant under the corresponding representation U of the symmetry group in H. The symmetry is then realized by the restriction of U to Φ and its contragradient representation U in Φ′. This double manifestation of the symmetry is related to the so‐called active and passive points of view commonly used for interpreting symmetry operations. Next, a general procedure is given for constructing a suitable space Φ out of the labeled observables of the system and the representation U describing its symmetry properties. This general method is then applied to the case where U is a semidirect product G = T[squaredtimes]Δ, with T Abelian. Finally, the examples of the Euclidean, the Galilei, and the Poincare groups are briefly studied.
58 citations
TL;DR: It is shown rigorously that no spontaneous ordering can occur; bounds on the order-order correlation function integrated over a subdomain indicate how the short-range order decays with distance.
Abstract: The ordering of one- and two-dimensional systems with a continuous symmetry is considered in the absence of a symmetry-breaking field. It is shown rigorously that no spontaneous ordering can occur; bounds on the order-order correlation function integrated over a subdomain indicate how the short-range order decays with distance.
13 citations
10 citations
TL;DR: In this paper, continuity arguments for transitions between various subgroups of the chiral symmetry group are presented, and some interesting sum rules are obtained in this way, where the transitions between subgroups are described as follows:
Abstract: Continuity arguments for transitions between various subgroups of the chiral-symmetry group are presented. Some interesting sum rules are obtained in this way.
10 citations
7 citations
6 citations
TL;DR: In this paper, models of spontaneous symmetry breakdown of SU(3) are discussed with the method of nonlinear realizations and with Kibble, and the superiority of the non-linear method is shown.
6 citations
TL;DR: In this paper, it is argued that approximate SU2×SU2 symmetry is expected on the grounds of the smallness of the pion mass together with some reasonably smooth behavior for matrix elements which involve a pion.
Abstract: The implications of the validity of chiralSU3×SU3 current algebra and the assumption that the chiral-symmetry breaking term transforms according to the (3,3*)+(3*, 3) representation ofSU3×SU3 are investigated. It is argued that approximateSU2×SU2 symmetry is expected on the grounds of the smallness of the pion mass together with some reasonably smooth behavior for matrix elements which involve a pion. The PCAC hypothesis, in its pole-dominance form, is applied to the π, K and ν cases in a step-by-step manner. Some results are obtained for the Kl3 form factors, includingf+(0)=1. Except for the equal-time commutation relations,SU3 symmetry is not invoked even approximately. Sum rules involvingfπ,fK,fν and the pseudoscalar-meson masses are derived, some of which differ significantly from those obtained by authors using approximateSU3 symmetry. In particular, an expression forfK/fπ is inferred which involves pseudoscalar-meson masses alone.
5 citations
TL;DR: In this article, a new estimate of a parameter in SU3×SU3 symmetry breaking was obtained, which confirmed earlier results on the relative magnitude of SU2×SU2 and SU3 symmetry violations.
TL;DR: Some Lagrangian models embodying both chiral symmetry and partial spin independence are proposed in this article, where the Lagrangians are invariant under covariant groups likeSL2,C orSL2.
Abstract: Some Lagrangian models embodying both chiral symmetry and partial spin independence are proposed. In the zero-mass limit for mesons, the Lagrangians are invariant under covariant groups likeSL2.C orSL2,C⊗SL2,C⊗U1⊗U1 in the case of no internal symmetry. The groups can be generalized toSL6,C orSL6,C⊗SL6,C. The symmetry is of the unconventional kind like chiral symmetry in so far as it does not respect the invariance of the vacuum or the stability of one-particle states. Pseudovector mesons transform nonlinearly with respect to spin trans-formations just as pseudoscalar mesons obey nonlinear-transformation laws in the case of chiral groups. Mesons that transform linearly and baryons can be classified by a compact subgroup of the covariant group. A definite way of breaking the symmetry leads to sum rules of the Weinberg type.
TL;DR: Finite dynamical symmetry transformations of the Kepler motion are given in closed analytic form in this article, where the symmetry transformations are expressed in terms of a closed-analytic form.
Abstract: Finite dynamical symmetry transformations of the Kepler motion are given in closed analytic form.
TL;DR: In this paper, the relativistic symmetry groups for all possible uniform electromagnetic fields are presented and discussed, and the symmetry groups are discussed in terms of relativistically symmetric groups.
Dissertation•
01 Jan 1969
TL;DR: In this article, an algebraic model describing symmetry breaking is applied to the weak meson decay and the suppression of the strangeness-changing weak decay is obtained as a consequence of symmetry breaking.
Abstract: An algebraic model describing symmetry breaking is applied to the weak meson decay. The suppression of the strangeness-changing weak decay is obtained as a consequence of symmetry breaking.
TL;DR: In this article, a Lagrangian model of SU3 symmetry is proposed for breakdown on a singular layer of the SU3 octet space as well as on the general layer, where gauge particles corresponding to broken components of the symmetry acquire mass while those corresponding to the little group of exact symmetries remain massless.
Abstract: We investigate a Lagrangian model ofSU3 symmetry that is applicable to breakdown on a singular layer ofSU3 octet space as well as on the general layer. In both cases, gauge particles corresponding to broken components of the symmetry acquire mass, while those corresponding to the little group of exact symmetries remain massless. We discuss the gauge-invariance properties of our model. including symmetry-breaking effects.
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TL;DR: The concept of symmetry is as old as Adam and Eve and observant individuals are well aware of the important role that symmetry plays in our physical environment as discussed by the authors, and as civilizations developed, it made a dramatic and decisive appearance here too.
Abstract: The concept of symmetry is as old as Adam and Eve, and observant individuals are well aware of the important role that symmetry plays in our physical environment. Symmetry has always been present in nature, and as civilizations developed, it made a dramatic and decisive appearance here too. This chapter will attempt to demonstrate the generality of the concept of symmetry, both in the natural and man-made aspects of our environment.
TL;DR: In this article, sum rules for spectral functions are obtained on the basis of the asymptoticSU petertodd3 symmetry breaking, the strong super-convergence of certain invariant amplitudes and the SU petertodd2×SU petertodd2 symmetry, using these sum rules, they obtain the ratioFK/Fππ=1.24, the Kl3 form factors ζ=−0.92, λ−=0.024 and the decay widths of the vector mesons.
Abstract: Several sum rules for the spectral functions are obtained on the basis of the asymptoticSU
3 symmetry breaking, the strong super-convergence of certain invariant amplitudes and the asymptoticSU
2×SU
2 symmetry. Using these sum rules, we obtain the ratioF
K/F
π=1.24, the Kl3 form factors ζ=−0.92, λ−=0.024 and the decay widths of the vector mesons. The results are in good agreement with experiment.
TL;DR: Gradshteyn and Jeffrey as discussed by the authors showed that even for tremendous values of H (the characteristic field m'c'/eh being 4.4X10\" G), the radiative correction to Eii remains of relative order 0.
Abstract: Eo= mc2+ (a/4n. )mc'f Dn(2ehH/m'c') —C——, ' j'+A+ ), (3) \"I.S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, edited by A. Jeffrey (Academic Press Inc. , Xew York, 1965). where C\"=0.577 is Euler's constant, and where .l is a numerical constant for which we have only found bounds: —6(A & 7. One readily sees from (3) that even for tremendous values of H (the characteristic field m'c'/eh being 4.4X10\" G), the radiative correction to Eii remains of relative order 0.. In particular, Eo certainly does not vanish at H= (4ir/n) (m,'c'/eh) = 7.6X10\" G, a field value for which (1) is not valid. Some doubts about the limits of validity of the anomalous magnetic moment concept have actually been raised by the authors of Ref. 2 themselves.
TL;DR: In this paper, the non-linear realization of the approximate chiral symmetry of the strong interactions is presented, and a nonlinear version of the chiral model is presented for strong interactions.
Abstract: The non-linear realization of the approximate chiral symmetry of the strong interactions is presented.