Showing papers on "Explicit symmetry breaking published in 1972"
TL;DR: In this article, the authors explore the possible origin of approximate mass formulas in theories based on spontaneously broken gauge symmetry, and show that such a model is untenable in the sense that manifest breaking of the gauge symmetry would destroy the renormalizability.
Abstract: There are a number of approximate relations among elementary particle masses. In conventional theories, these are explained by assuming a hierarchy of interactions with the property that the stronger interactions have the more extensive symmetry. In renormalizable theories based on spontaneously broken gauge symmetry, this view is untenable. Manifest breaking of the gauge symmetry would destroy the renormalizability. We explore the possible origin of approximate mass formulas in theories of this kind.
70 citations
43 citations
TL;DR: In this paper, it was shown that in absence of spontaneous breaking, in the presence of spontaneous breakings, dilatations are incompatible with conformal invariance and positivity.
16 citations
15 citations
TL;DR: In this paper, the s-channel isospin zero A-amplitude in off-mass-shell kaon-nucleon scattering is investigated at the crossing-symmetric point by evaluating a finite-energy sum rule.
15 citations
TL;DR: In this article, the authors apply tensor algebra to the permutational symmetry of the permutation group of the N$-electron problem and give a further reduction of what is normally regarded as the reduced matrix element with respect to spatial symmetry alone.
Abstract: The techniques of tensor algebra customarily applied to exploit spatial symmetry are applied to exploit permutational symmetry of the $N$-electron problem. In the approximation of no spin-orbit coupling, the results are nontrivial and give a further reduction of what is normally regarded as the reduced matrix element with respect to spatial symmetry alone. The required $3\ensuremath{-}j$ coefficients of the permutation group are evaluated in an appendix so that intermediate group-theoretical indices that have no direct physical significance are eliminated from the formulation. The spin integral for any operator can always be reduced to known integrals of the fundamental Pauli operators. Thus all matrix elements can be reduced to a corresponding spin-free form with known weighting coefficients. An explicit expression is given for the matrix element of an operator suitable for evaluating spin-own-orbit coupling or spin density at the nucleus. A recursion relation for the Clebsch-Gordan coefficients of bipartition representations of ${S}_{N}$ in terms of its subgroups and the $9\ensuremath{-}j$ sympols of $\mathrm{SU}(2)$ is developed in the appendix. For one of the representations being the totally symmetric representation, the Clebsch-Gordan coefficient is known and the recursion relation (the group-orthogonality relation in this case) can be considered as giving nontrivial sum rules on the $9\ensuremath{-}j$ symbols of $\mathrm{SU}(2)$.
14 citations
TL;DR: In this article, a spectral measure involving the lowest two moments of the Hamiltonian is examined to see if it provides on the average an accurate description of the breaking of group symmetry in nuclei.
11 citations
11 citations
01 Jan 1972
TL;DR: In this article, a few macroscopic aspects of irreversibility and nonlinear eigenvalue problems are discussed, on a rather phenomenological level but hopefully these problems will be taken up in the near future from a more sophisticated many body or kinetic theory point of view.
Abstract: We shall discuss in these lectures a few macroscopic aspects of irreversibility and nonlinear eigenvalue problems. We shall. remain on a rather phenomenological level but hopefully these problems will be taken up in the near future from the more sophisticated many body or kinetic theory point of view.
7 citations
TL;DR: In this article, it was shown that the Kπ scattering data is incompatible with the SU(3) symmetry of the vacuum, and it is concluded that, within this scheme, the kπ data is not consistent with the symmetry.
TL;DR: In the SU(3) limit, a second class, T-normal axial vector current, which transforms like an octet, can give rise to pseudotensor terms in the matrix elements for leptonic decays of baryons.
TL;DR: In this paper, the symmetry of a crystal with an ideal surface is investigated and it is shown that the two-dimensional space group symmetry of the crystal should be used rather than the pure translational symmetry.
TL;DR: In this paper, the scale dimension of the chiral symmetry breaking Hamiltonian was determined to be d u = 2 by using the experimental information on the forward differential cross section for high energy ps. meson photoproduction under the assumption of the P.C.A.
TL;DR: In this article, the authors present an alternative scheme which provides a simple understanding of yet unexplained features of baryon resonance data, and which implies a qualitative breaking of SU3 for Baryon Resonance decay rates.
TL;DR: In this article, the authors considered the symmetry limit in the tree approximation to the σ-sigma model and analyzed the implications of this for the existence of a radius of convergence for perturbation expansions about symmetry limit.
Abstract: In the tree approximation to the $\ensuremath{\sigma}$ model the scalar-field vacuum expectation values are multi-valued functions of the symmetry-breaking parameters. The implications of this for the existence of a radius of convergence for perturbation expansions about the symmetry limit are analyzed. Special attention is given to the structure of the solutions as a function of the mass parameter in the original Lagrangian. Although this parameter is numerically small in a fit to data, its precise value determines whether the underlying symmetry-limit solution can exhibit spontaneous breakdown of the symmetry. The mathematical structure of the solutions is surprisingly similar to that of the mean-field theory in statistical mechanics. It is suggested that the real world may be near a "phase transition" and that new methods in statistical mechanics could be exploited to analyze chiral dynamics, with results more general than found in the particular model considered here.
TL;DR: Hadron currents are introduced in this article which violate the chiral SU (3) × SU(3) algebra, but leave the subalgebra of SU(2) + SU(1) unchanged.
TL;DR: In this paper, the Cabibbo rotation in models of chiral symmetry breaking is considered and the results are independent of the chiral properties of the symmetry breaking and the second method is inconsistent in the (8, 8) and (6, 6¯) + (6¯, 6) models.
TL;DR: In this article, the singularities of expansions in the symmetry-breaking parameters of chiral and scale-asymmetric theories are studied, in the tree approximation, in polynomial Lagrangian models.
Abstract: Singularities of expansions in the symmetry-breaking parameters of chiral- and scale-asymmetric theories are studied, in the tree approximation, in polynomial Lagrangian models. The singularities are related to the appearance of zero-mass scalar fields, not necessarily Goldstone particles, at the radius of convergence of the expansion. Methods of avoiding these singularities are presented.
Journal Article•
TL;DR: In this article, a model that unifies the intermediate boson of the weak interaction and the photon of the electromagnetic interaction into a multiplet of gauge fields is considered and the $K$-spin-triplet hypothesis emerges from such an approach.
Abstract: A model that unites the intermediate boson of the weak interaction and the photon of the electromagnetic interaction into a multiplet of gauge fields is considered. Weak leptonic currents and hadronic Cabibbo currents are handled in a parallel manner and generate an SU(2) symmetry group. It is suggested how the $K$-spin-triplet hypothesis emerges from such an approach. The symmetry between the weak and electromagnetic interaction is spontaneously broken resulting in a massive electron and an intermediate boson.
NEC1
TL;DR: In this article, the effect of spontaneous symmetry breaking in the critical region of phase transition has been considered, where the symmetry breaking appearing locally above the critical temperature T c increases its coherence length and life time to infinity.
Abstract: Hydrodynamics is developed in the critical region of phase transition by noticing that the effect of spontaneous symmetry breaking must fully be taken into account there, where the symmetry breaking appearing locally above the critical temperature T c increases its both coherence length and life time to infinity as temperature T approaches T c . It is predicted that an energy density wave will finally be observed as we approach arbitrarily close to T c from above. In magnets, only the diffusive excitation of local magnetization is expected if the observation takes place during a finite time which is much larger than the life time τ SB of the local symmetry breaking above T c . This situation of observation cannot be realized in the limit T → T c since the life time τ SB diverges in the same limit. On the other hand, if the time needed for the observation is less than the life time τ SB specifically in the critical region, the alternative hydrodynamic excitation to be observed is an energy density wave.
TL;DR: In this article, the spectral function sum rule for the vacuum expectation value of the chiral symmetry-invariant scale-breaking part of the Hamiltonian density u(x) was derived from the assumption that u has a dimension.
TL;DR: In this article, the failure of symmetry predictions for two-body inelastic processes at high energy is assumed to arise from massdifference effects in the t-channel, and a new prescription for cross-sections comparison is presented.
TL;DR: In this paper, an alternate method for determining the number of times a given symmetry species will occur in the reducible representation of a particular molecule that requires no previous knowledge of the symmetry species that are allowed is presented.
Abstract: Presents an alternate method for determining the number of times that a given symmetry species will occur in the reducible representation of a particular molecule that requires no previous knowledge of the symmetry species that are allowed.
TL;DR: A hierarchy of possible symmetries in quantum field theory is defined in this article, which reaches from a purely mathematical invariance to the conventional physical invariance, including the commonly discussed type of spontaneously broken symmetry (SBS).
TL;DR: In this article, the authors report supplementary remarks to some earlier papers (1) concerning epochs in which the evolution of the universe can be described as a quasi-adiabatic expansion, and the symmetry problem of the conformal group and, in the 3D space, of the SOt group arises.
Abstract: In this note we report supplementary remarks to some earlier papers (1). The first group of remarks concerns epochs in which the evolution of the Universe can be described as a quasi-adiabatic expansion. For the zero-mass constituent, like neutrinos and photons, the symmetry problem of the conformal group and, in the 3-dimensional space, of the SOt group arises. In the second part of this report we shall be concerned with the cut-off problems and the commutation relations. Starting with the Einstein equations with the cosmological constant A,