Showing papers on "Explicit symmetry breaking published in 1967"
TL;DR: In this paper, the authors studied the symmetry of scattering amplitudes at vanishing momentum transfer and derived a one-parameter "mass formula" describing the deviation of the slopes of Regge trajectories from the value required by the higher symmetry.
Abstract: We study the symmetry of scattering amplitudes at vanishing momentum transfer. We show that the little group of the Poincar\'e group corresponding to vanishing four-momentum (isomorphic to the homogeneous Lorentz group, or, by analytic continuation, to the four-dimensional rotation group) is in general not a symmetry of the scattering amplitude. However, the spectrum of the amplitude is classified according to the larger symmetry. Regge poles occur in families; the members of the family follow the first one in integer steps at vanishing momentum transfer and are classified according to a new quantum number derived from the higher symmetry. We derive a one-parameter "mass formula" describing the deviation of the slopes of Regge trajectories from the value required by the higher symmetry. The theory is applied to the problem of the high-energy scattering of particles of arbitrary mass, and leads to an unambiguous asymptotic expression for the scattering amplitude. We analyze the implications of the new symmetry for the spectrum of hadrons. The predicted new Regge trajectories lead to observable particles and resonances; their coupling strength is determined by the symmetry in terms of the parameters of the "parent" trajectories. In particular we assign the ${N}^{\ensuremath{'}}(1400)$ resonance to the second "daughter" of the ${N}_{\ensuremath{\alpha}}$ trajectory; the symmetry breaking turns out to be small, and the decay width of ${N}^{\ensuremath{'}}(1400)$ is computed in satisfactory agreement with the experimental result.
68 citations
TL;DR: In this paper, it was pointed out at the Seventh International Congress of Crystallography in Moscow 1966 (Informal Session on the Powder Intensity Project), it is very desirable to have a standard powder specimen for X-ray intensity measurements, because with such a specimen a relative measurement can readily be converted to an absolute one.
Abstract: 1964), although in these two examples the reduction already almost vanishes at the second reflexion, which is very close to the first one in angular position. The reduction found in the present study, however, is too small to conclude therefrom the existence of solid state effects. It is also to be mentioned that the present X-ray diffraction data do not give any information about the region below sin 0/2 = 0.25 A -1. It is apparent that the contradictory results found by various authors are related to the techniques used for determining the intensity data on the absolute basis. In measurements of this kind, it is necessary to pay much attention to detailed experimental conditions. For example, we have found that an inaccuracy of + 0.2 ° (in 20) in the zero alignment (Batterman et al., 1960) may result in an error of + 5% in the integrated intensity when 0 = 10 °, if the receiving slit is very narrow. As was pointed out at the Seventh International Congress of Crystallography in Moscow 1966 (Informal Session on the Powder Intensity Project), it is very desirable to have a standard powder specimen for X-ray intensity measurements, because with such a specimen a relative measurement can readily be converted to an absolute one. In the light of our measurements, carbonyl iron seems to be suitable for the purpose. This powder is stable, and identical specimens will be available in different laboratories because of a well standardized procedure for the preparation of this substance.
26 citations
21 citations
TL;DR: In this article, an orthonal separation of the Hamiltonian operator into parts which preserve and break a given symmetry is introduced, along with norms for measuring the separate components, taking full account of the restrictions imposed by the exact symmetries.
18 citations
TL;DR: The mechanism of spontaneous breakdown of continuous internal symmetries in relativistic quantum field theories in which Coulomb-type potentials are not initially present is studied in this paper.
Abstract: The mechanism of spontaneous breakdown of continuous internal symmetries is studied in relativistic quantum field theories in which Coulomb-type potentials are not initially present. The crucial point is the analysis of the structure of the symmetry generators in terms of the physical (asymptotic) fields, which can be performed without solving the dynamical problem explicitly. Mathematically, spontaneous breakdown of symmetry is possible when the symmetry transformations are not required to be unitarily implementable in the physical Hilbert space. It is shown that failure of implementability results exclusively from linear contributions of massless spin-zero physical fields to the generators. The breakdown of symmetry is exhibited in an asymmetric vacuum state; however, mass differences within multiplets of physical fields are found to be forbidden. Asymmetry of the vacuum is, in physical language, the result of Bose-Einstein condensation of massless, spinless physical bosons, which acts as the source of spurions.
17 citations
TL;DR: In this paper, a detailed analysis is given of quark-model predictions which are equivalent to those from higher symmetries even though no symmetry is explicitly assumed, and general rules for obtaining symmetry results without detailed calculations, and the implications of symmetry breaking are discussed.
16 citations
TL;DR: By making use of squared parabolic coordinates, SU(2) ⊗ SU (2) symmetry of the Kepler motion is demonstrated in a straightforward way in this article, where the symmetry is derived in a natural manner, and a similarity between their approach and current algebra is pointed out.
15 citations
CERN1
TL;DR: In this paper, partial wave dispersion relations with crossing symmetry have been used to test the validity of the bootstrap hypothesis, the dynamical generation of symmetries and Dashen-Frautschi perturbation theory.
Abstract: Assuming that the physical world is a solution of theS matrix equations, nonlinear functional analysis enables its uniqueness to be tested experimentally. As a first step, we develop such tests within the limits of partial wave dispersion relations,with crossing symmetry included. They are closely related to Levinson's theorem. We show that they give conditions for the validity of the bootstrap hypothesis, of the dynamical generation of symmetries, and of Dashen-Frautschi perturbation theory. They do not appear to be satisfied experimentally.
15 citations
Journal Article•
TL;DR: In this paper, the Bethe-Salpeter equation for spinor quark-antiquark binding in the ladder approximation was studied in terms of projective variables, which exhibit the maximal symmetry of the problem as an O5 symmetry for special values of masses involved.
Abstract: The Bethe-Salpeter equation for spinor quark-antiquark binding in the ladder approximation is studied in terms of projective variables. These variables exhibit the maximal symmetry of the problem as anO5 symmetry for special values of masses involved. The realistic Bethe-Salpeter equation is treated as corresponding to a brokenO5 symmetry situation. Among other advantages of this approach is that the continuum eigenvalue difficulties for the bound states encountered in other treatments seem obviated.
TL;DR: In this article, a statistical soft-meson model combined with unitary symmetries is proposed to account for a number of observed properties in high-energy large-angle scattering, and a method for extracting that part of the cross section which should not be sensitive to symmetry breaking is discussed.
TL;DR: In this article, the symmetry properties of nonlinear dielectric tensors in crystals are considered by means of an essentially thermodynamic procedure, and symmetry properties which arise in nonabsorbing non-nondispersive media are discussed.
Abstract: Symmetry properties of nonlinear dielectric tensors in crystals are considered. In particular, symmetry properties which arise in nonabsorbing nondispersive media are discussed by means of an essentially thermodynamic procedure.
TL;DR: In this paper, a partitioning technique is developed according to which the Hamiltonian is split into an unperturbed part, which is totally symmetrical with respect to a chosen group of symmetry operations and a symmetry-breaking perturbation coupling the states of different symmetries.
TL;DR: In this paper, the invariants constructed of quantities transforming as representations of the Lorentz group are shown to be possibly classified according to representations of SL(3C) or SU3.
TL;DR: In this article, it was shown that in the symmetry with a non-compact group, there exists no contradiction with the unitarity condition of the S-matrix, and that the symmetry is crossing-symmetrical.
Abstract: We study the non-compact symmetry groups and their connections with field theory. We prove explicity that in the symmetry with a non-compact group there exists no contradiction with the unitarity condition of theS-matrix. We have suggested a method of describing the symmetry with a non-compact group by means of the apparatus of the local quantum field theory. Within our method the field operators satisfy the normal commutation relations, and theS-matrix is crossing-symmetrical.
TL;DR: In this article, the authors examined the non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering.
Abstract: We examine the recently proposed non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering. We give a very general realization of the corresponding infinite dimensional Lie algebra in the Fok space of asymptotic states built from two scalar nucleons. Assuming that the algebra describes the exact symmetry of theS-matrix we conclude that no elastic NN scattering exists.
TL;DR: In this paper, an algebraic procedure leading to all the geometric symmetry operations of a given set of points is described, which is the basis for our algebraic approach to geometric symmetry.
Abstract: An algebraic procedure leading to all the geometric symmetry operations of a given set of points is described.
TL;DR: In this article, the quasi-particle method is applied to an SU3 symmetric four-fermion interaction between octet-baryons N and antibaryons n (of between quarks and antiquarks).
01 Jan 1967
TL;DR: The SU(4) symmetry group of nuclear interaction was first proposed by Wigner as discussed by the authors, where the nuclear forces are independent not only of the orientation in isospin space but also of the ordinary-spin orientation of the nucleons.
Abstract: Twenty-seven years ago, Wigner proposed the SU(4) theory of nuclear forces.1 It was suggested that the nuclear forces are independent not only of the orientation in isospin space but also of the ordinary-spin orientation of the nucleons. Thus, it does not matter whether the interacting particle is p ↑ or p ↓, or n ↑ or n ↓ ( ↑ and ↓ refer respectively to the third component, “up” or “down,” of the spin). This leads to the SU(4) symmetry group of nuclear interaction, with the four I = ½, S = ½ nucleons belonging to the basic four-dimensional representation.† In this theory, one encounters for the first time a “marriage” of an internal symmetry group, in this case the SU(2) isospin group, with the ordinary-spin SU(2) group. Recently, Gursey, Radicati, and Pais2 and, independently, Sakita3 have proposed an SU(6) theory for strongly interacting particles (hadrons) in which the basic ideas are quite similar to Wigner’s SU(4) theory. One again fuses the internal symmetry group for hadrons with the ordinary spin. The internal symmetry group is, of course, taken to be SU(3), since this has emerged as the “right generalization” of the isospin SU(2) group for hadrons.
TL;DR: In this article, a model for leptonic decays using unitary symmetry was considered, and a special method of symmetry-breaking was applied taking into account all corrections due to baryon mass differences.
Abstract: A model for leptonic decays is considered using unitary symmetry. For the calculation of matrix elements a special method of unitary symmetry-breaking is applied taking into account all corrections due to baryon mass differences.
TL;DR: In this article, the authors investigated symmetry breaking solutions of several model theories with the result that constant gauge transformations of the fields describing zero mass Goldstone particles are responsible for the formal possibility of spontaneous symmetry breaking.
Abstract: Symmetry breaking solutions of several model theories are investigated with the result that constant gauge transformations of the fields describing zero mass Goldstone particles are responsible for the formal possibility of the spontaneous symmetry breaking.
TL;DR: An example of a combination of spontaneous and intrinsic breakdown of symmetry is studied in this article, where the effect of spontaneous breakdown is much stronger than that of intrinsic breakdown, the original symmetry is replaced by a new symmetry and the symmetry transformation is mainly taken care of by the transformation of spinless boson.
Abstract: An example of a combination of spontaneous and intrinsic breakdown of symmetry is studied. When the effect of spontaneous breakdown is much stronger than that of intrinsic breakdown, the original symmetry is replaced by a new symmetry and the symmetry transformation is mainly taken care of by the transformation of spinless boson. When the intrinsic breaking term becomes stronger, the symmetry transformation comes closer to its original form, while the spinless boson remains. The divergence of helicity current written in terms of physical field is obtained in the form effectively similar to PCAC. A possible application to the spurion theory of the weak phenomena is suggested.