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Showing papers on "Symmetry (physics) published in 1970"


Journal ArticleDOI
TL;DR: In this paper, a model of weak interactions was proposed in which the currents are constructed out of four basic quark fields and interact with a charged massive vector boson, and it was shown that the leading divergences do not violate any strong-interaction symmetry.
Abstract: We propose a model of weak interactions in which the currents are constructed out of four basic quark fields and interact with a charged massive vector boson. We show, to all orders in perturbation theory, that the leading divergences do not violate any strong-interaction symmetry and the next to the leading divergences respect all observed weak-interaction selection rules. The model features a remarkable symmetry between leptons and quarks. The extension of our model to a complete Yang-Mills theory is discussed.

2,055 citations


Book
01 Jan 1970

597 citations


Journal ArticleDOI
TL;DR: In this article, a general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed, besides the well-known Ising and "ice" models, other soluble cases are also considered.
Abstract: A general lattice-statistical model which includes all soluble two-dimensional model of phase transitions is proposed. Besides the well-known Ising and "ice" models, other soluble cases are also considered. After discussing some general symmetry properties of this model, we consider in detail a particular class of the soluble cases, the "free-fermion" model. The explicit expressions for all thermodynamic functions with the inclusion of an external electric field are obtained. It is shown that both the specific heat and the polarizability of the free-fermion model exhibit in general a logarithmic singularity. An inverse-square-root singularity results, however, if the free-fermion model also satisfies the ice condition. The results are illustrated with a specific example.

335 citations


Journal ArticleDOI
TL;DR: In this paper, the case of symmetry breaking by a term linear in Bose fields (source term) is analyzed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and the ground state energy density as a function of the strength of the source term.
Abstract: If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.

230 citations


Journal ArticleDOI
TL;DR: In this paper, time-dependent invariants for a nonstationary harmonic oscillator and for a charged particle in a varying axially symmetric classical electromagnetic field are found, and the Green's functions are obtained in closed form.
Abstract: New time-dependent invariants for the $N$-dimensional nonstationary harmonic oscillator and for a charged particle in a varying axially symmetric classical electromagnetic field are found. For these quantum systems, coherent states are introduced, and the Green's functions are obtained in closed form. For a special type of electromagnetic field which is constant in the remote past and future, the transition amplitudes between both arbitrary coherent states and energy eigenstates are calculated and expressed in terms of classical polynomials. The adiabatic approximation and adiabatic invariants are discussed. In the special case of a particle with time-dependent mass, the solution of the Schr\"odinger equation is found. The symmetry of nonstationary Hamiltonians is discussed, and the noncompact group $U(N, 1)$ is shown to be the group of dynamical symmetry for the time-dependent $N$-dimensional oscillator.

204 citations


Book
01 Jan 1970

200 citations


Journal ArticleDOI
TL;DR: In this article, Kneer's method for obtaining polycrystal elastic constants from single crystal constants and orientation distribution is extended to orthotropic physical symmetry (rolled sheet) and to cubic crystal symmetry.

148 citations


Journal ArticleDOI
TL;DR: In this paper, a method was described whereby molecular symmetry is used to reduce the number of integrals which must be stored and processed in SCF calculations, which reduced the complexity of SCF calculation.

88 citations



Journal ArticleDOI
TL;DR: In this article, the problems associated with η-X mixing and η → 3 π in a chiral lagrangian framework, assuming a basic (3, 3 ) + 3, 3 + 3, 3 ) symmetry breaking of SU(3) × SU (3) and that ΔI = 1 electromagnetic processes are dominantly described by an effective u 3 type interaction, are reviewed.

61 citations


Journal ArticleDOI
E. Plahte1
TL;DR: In this paper, the dual tree-graph N-point functions are investigated from the point of view of symmetry properties using a cyclic symmetric-contour integral forBN.
Abstract: The dual tree-graphN-point functions are investigated from the point of view of symmetry properties. Using a cyclic symmetric-contour integral forBN, we deduce a set of simple relations betweenN—1BN-functions and give rules for writing down more complicated relations. Secondly, we establish a new relationship between the cyclic symmetric integral and the conventional “multiperipheral” integral forBN. Finally, both approaches are used to investigate the signature properties ofBN.

Journal ArticleDOI
TL;DR: In this article, the authors review spatially homogeneous, axially symmetric universes containing either an ideal fluid (with a γ-law equation of state) or a uniform magnetic field parallel to the symmetry axis or both.
Abstract: We review spatially homogeneous, axially symmetric universes containing either an ideal fluid (with a γ‐law equation of state) or a uniform magnetic field parallel to the symmetry axis or both. In many cases, the field equations may be solved by the technique (described in detail) of replacing the cosmic time by a suitably chosen timelike parameter. We systematically derive all known exact solutions for such universes.

Journal ArticleDOI
TL;DR: In this article, the dispersion curves on zinc blende measured by neutron scattering are presented for the symmetry directions, and the results are compared to calculations on a rigid ion model and a shell model.

Journal ArticleDOI
TL;DR: In this paper, the spectral properties of an extended molecular system, such as a linear polymer, are considered in terms of the linear response tensor (LRT), which determines the part of the average current density that is proportional to the transverse electric field.
Abstract: The spectral properties of an extended molecular system, such as a linear polymer, are considered in terms of the linear response tensor (LRT) which determines the part of the average current density that is proportional to the transverse electric field. In order to formulate such phenomena as optical rotatory dispersion (ORD) and circular dichroism (CD) use is made of Maxwell's equation for the transverse field components. Periodic boundary conditions are used for both the molecular system and the radiation field. The symmetry properties of the LRT with respect to time translation, time reversal, and reversal of propagation direction of the photon are given. Discussion is given of the relation between the components of the LRT and various optical properties such as ORD, CD, and linear birefringence. For an extended molecular system, having discrete symmetry operations (e.g., translations or screw axis), it is shown that a multicenter expansion is useful for formulating the LRT in terms of unit‐cell space...

Journal ArticleDOI
TL;DR: In this paper, the lattice dynamics of cuprite at the centre of the Brillouin zone is studied and the force constants and the effective charge of the crystal are deduced.
Abstract: A study of the lattice dynamics of cuprite at the centre of the Brillouin zone is made and the force constants and the effective charge deduced The energies of the optically inactive phonons are calculated and their symmetry determined The symmetry of the upper valence band of the crystal is identified

Journal ArticleDOI
TL;DR: The Hartree-Fock problem is investigated by examining the symmetry properties of the SCF spin-orbitals in this article, and the effect of symmetry-breaking in spin, angular momentum and space-group symmetry is considered schematically and the physical implications of such symmetry breaking are discussed.

Book ChapterDOI
TL;DR: In this article, the symmetry properties of reduced density matrices and natural p -states resulting from a given symmetry behavior of the wave functions, from which the density matrix are constructed, are discussed.
Abstract: Publisher Summary This chapter discusses symmetry properties of reduced density matrices and natural p -states resulting from a given symmetry behavior of the wave functions, from which the density matrices are constructed. Symmetry properties of p- densities are defined as the diagonal elements of the corresponding density matrices. Reduced density matrices have received increasing interest in quantum-chemical investigations. On one hand, numerical first- and second-order density matrices (one- and two-particle density matrices) for certain states of simple atomic and molecular systems have been calculated starting from rather good approximate wave functions. These matrices are particularly useful for testing the validity of different wave functions of the same system. Different approximations are most conveniently compared in terms of the eigenstates of these matrices— that is, the natural spin-orbitals and natural spin-geminals as well as the corresponding eigenvalues, the occupation numbers. On the other hand, the general properties of these matrices and their eigenstates— that is, those properties that are independent of the nature of the wave functions used in their construction, are especially interesting and some effort has been spent on studying them.

Journal ArticleDOI
TL;DR: In this paper, the frequency against wave vector dispersion relations were studied for waves travelling along three symmetry directions (100, (110), and (111) for copper, silver and gold using a modified non-central force model, which took into account the effect of electron-ion interaction also.
Abstract: The frequency against wave vector dispersion relations are studied for waves travelling along three symmetry directions (100), (110) and (111) for copper, silver and gold using a modified non-central force model, which takes into account the effect of electron-ion interaction also. The theoretical results are compared with the inelastic neutron scattering results for copper and silver, and are found to be in good agreement. A good agreement for gold is also anticipated. The contribution of angular interactions to the Cauchy discrepancy has been emphasized.

Journal ArticleDOI
TL;DR: In this paper, the relative merits of statistical factors and symmetry numbers in transition state theory are discussed in relation to potential energy surfaces with valley bifurcations, and conditions for the applicability of the two methods are considered in terms of the details of the motion at the bifurlcation, and some examples are discussed.
Abstract: The relative merits of statistical factors and symmetry numbers in transition state theory are discussed in relation to potential energy surfaces with valley bifurcations. Conditions for the applicability of the two methods are considered in terms of the details of the motion at the bifurcation, and some examples are discussed.

Journal ArticleDOI
TL;DR: In this article, the action of a local internal symmetry on the asymptotic states is determined using the Haag-Ruelle construction and a condition of "asymptotic locality" is derived.
Abstract: Symmetries are investigated from the local viewpoint. Using the Haag-Ruelle construction, the action of a local internal symmetry on the asymptotic states is determined. A condition of “asymptotic locality” is derived and used to show that the symmetry acts linearly and locally on the asymptotic fields. Within a field theoretical framework it is shown that the internal symmetry must commute with the Poincare group. The general structure of an internal symmetry is determined. The uniqueness of the representation of the Poincare group is discussed, and a simple example of an infinite component field is given to indicate what occurs when there are infinitely degenerate particle multiplets.

Journal ArticleDOI
TL;DR: In this paper, the four-nucleon transfer reaction induced by 10 B on 12 C has been studied above the Coulomb barrier, and the population of final states of 16 O is less selective than in other 4N transfer reactions induced by 6 Li, 7 Li, or 16 O. This fact can be explained by the complexity of the structure of the ground state of 10 B, which has large components with a lower degree of symmetry than the α-particle.

Journal ArticleDOI
TL;DR: In this article, the soft-meson theorems for all scattering amplitudes of the pseudoscalar octet, with two particles off shell, employing PCAC, were given.



Book ChapterDOI
01 Jan 1970
TL;DR: In the absence of matter, there is naturally no centrally-symmetric solution as the free gravitational field cannot have such symmetry as discussed by the authors, and the solution obtained for the centrally symmetrical problem is actually a particular case of a more general class of solutions.
Abstract: Publisher Summary This chapter examines the general properties of the cosmological solutions of the gravitational equations near a time singularity. The customarily used (Friedmann) cosmological solution of Einstein's gravitational equations is based on the assumption that matter is distributed in space homogeneously and isotropically. This assumption is very far-fetched mathematically, apart from the fact that its fulfillment in a real world can at best be only approximate. The solution obtained for the centrally symmetrical problem is actually a particular case of a more general class of solutions. In the absence of matter, there is naturally no centrally-symmetrical solution as the free gravitational field cannot have such symmetry.

Journal ArticleDOI
TL;DR: In this article, a unified theory of the weak and electromagnetic interactions of leptons and hadrons is constructed, and the underlying symmetry group is taken to be the $\mathrm{SU}(2)$ generated by the weak lepton currents and the hadronic Cabibbo currents.
Abstract: A unified theory of the weak and electromagnetic interactions of leptons and hadrons is constructed. The underlying symmetry group is taken to be the $\mathrm{SU}(2)$ generated by the weak lepton currents and the hadronic Cabibbo currents. This symmetry is destroyed by the spontaneous breakdown mechanism. In our theory, the weak coupling constant is the same as the electromagnetic coupling constant, and the mass of the charged intermediate boson is 37.4 GeV.


Journal ArticleDOI
TL;DR: In this article, the De Launay type angular force model has been applied to sodium to study the dispersion relations in the three symmetry directions, and the theoretical results are compared with the experimental ones obtained from inelastic neutron scattering.
Abstract: De Launay type angular force model has been applied to sodium to study the dispersion relations in the three symmetry directions. Electron-ion interaction has also been taken into account. The theoretical results are compared with the experimental ones obtained from inelastic neutron scattering and an excellent agreement has been obtained. The Cauchy discrepancy is attributed to the presence of both types of non-central interactions.

Journal ArticleDOI
TL;DR: The application of Rayleigh's treatment of capillary stability to the case of an inviscid liquid bounded by two concentric circular cylindrical surfaces leads to a characteristic equation from which the following predictions can be made as mentioned in this paper.
Abstract: The application of Rayleigh's treatment of capillary stability to the case of an inviscid liquid bounded by two concentric circular cylindrical surfaces leads to a characteristic equation from which the following predictions can be made The system is stable for disturbances that do not have cylindrical symmetry It is stable (unstable) for disturbances with cylindrical symmetry when the wavelength of the disturbance in axial direction is less (greater) than the circumference of the inner surface There are always two modes of deformation In the special case of a thin‐walled cylinder these two modes are symmetric and antisymmetric, respectively When the wavelength of the disturbance is varied in such a manner that there is a transition from stable to unstable conditions, then at the same time there is a transition from symmetric to antisymmetric mode or vice versa It is shown, further, that when one mode is stable and the other unstable, the stable mode is a deformation for which the total surface area of the system is increased by the disturbance, while the unstable mode corresponds to decreased surface area

Journal ArticleDOI
TL;DR: In this article, the spontaneous breakdown of a continuous symmetry group generated by conserved currents is considered in the framework of general quantum field theory and a general relation is derived between n− and (n+1) point functions involving Goldstone bosons.