Showing papers on "Symmetry (physics) published in 1973"
TL;DR: In this article, the authors show that perturbation theory is arbitrarily good for the deep Euclidean Green's functions of any Yang-Mills theory and of many Yang Mills theories with fermions.
Abstract: An explicit calculation shows perturbation theory to be arbitrarily good for the deep Euclidean Green's functions of any Yang-Mills theory and of many Yang-Mills theories with fermions. Under the hypothesis that spontaneous symmetry breakdown is of dynamical origin, these symmetric Green's functions are the asymptotic forms of the physically significant spontaneously broken solution, whose coupling could be strong.
2,826 citations
TL;DR: In this paper, the renormalization-group equations are derived for Yang-Mills theories and the parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free.
Abstract: Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization-group techniques and their application to scaling phenomena. The renormalization-group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large spacelike momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3) \ifmmode\times\else\texttimes\fi{} SU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken and that the severe infrared singularities prevent the occurrence of noncolor singlet physical states. The deep-inelastic structure functions, as well as the electron-positron total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive light-cone or parton-model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
1,232 citations
TL;DR: In this article, the one-loop contributions to fermion and pseudo-Goldstone masses are calculated for the general class of renormalizable guage theories, and it is shown explicitly that when the masses are subject to any type of zeroth-order symmetry.
Abstract: The one-loop contributions to fermion and pseudo-Goldstone masses are calculated for the general class of renormalizable guage theories. It is shown explicitly that when the masses are subject to any type of zeroth-order symmetry. relation for all values of the parameters in the Lagrangian, the divergences in the one-loop corrections to these symmetry relations cancel. The finite parts of these corrections are evaluated and discussed. Other topics considered include the connection of this work with that of Coleman and E. Weinberg, the constraints obeyed by scalar coupling constants, and the path-integral derivation of the Feynman rules for general renormalizable gauge theories.
209 citations
01 Feb 1973
TL;DR: In this paper, a generalization of Floquet's theorem is presented for periodically loaded closed waveguides possessing a certain class of higher symmetries which includes the screw and glide symmetry.
Abstract: A generalization of Floquet's theorem is presented for periodically loaded closed waveguides possessing a certain class of higher symmetries which includes the screw and glide symmetries. These symmetries frequently appear in microwave structures such as filters, traveling-wave tubes, and traveling-wave antennas. The theorem states that the natural modes are eigenvectors of the symmetry operator characterizing the structure. An alternative derivation of the theorem using an equivalent network representation leads naturally to a simple method for constructing the qualitative dispersion (Brillouin) diagrams for structures with screw or glide symmetry.
155 citations
139 citations
134 citations
TL;DR: In this article, a modification of the Veneziano model incorporating SU(N) symmetry in a dynamical fashion is shown to have critical dimension 26−N. The spectrum generating algebra is constructed and used to prove the no-ghost theorem for space-time dimension d ⩽ 26.
116 citations
88 citations
TL;DR: The symmetry factor and the transfer coefficient in electrode reactions have fundamentally different significance as discussed by the authors, and the symmetry factor has been shown to have significant importance in both the transfer and symmetry factors.
Abstract: The symmetry factor and the transfer coefficient in electrode reactions have a fundamentally different significance.
87 citations
TL;DR: Based on the particle-plus-rotor model, it was shown that a new coupling scheme should occur in nuclei under certain conditions as discussed by the authors, in which j is quantized along the direction of I rather than along the symmetry axis.
77 citations
01 Jan 1973
TL;DR: In this paper, the existence of a critical curve of fixed points of a renormalization group acting on a space of coupling constants is proved, and on this curve all nonsoft axial vector and scaling anomalies vanish.
Abstract: Renormalized Ward identities and Callan-Symanik equations are dcveloped for vertex functions involving composite fields in a massive Thirring model with U(n) symmetry. The existence of a critical curve of fixed points of a renormalization group acting on a space of coupling constants is proved. On this curve all nonsoft axial-vector and scaling anomalies vanish. Attraction properties of this curve are investigated. The possibility of a second critical curve for strong coupling is discussed. (auth)
TL;DR: In this paper, the distribution of thermal stress in an anisotropic elastic half-space is derived for the case when the temperature and stress fields are independent of one of the three Cartesian coordinates.
Abstract: Equations for the distribution of thermal stress in an anisotropic elastic half-space are derived for the case when the temperature and stress fields are independent of one of the three Cartesian coordinates. These equations are used to determine the stress field due to an arbitrary temperature distribution and particular stress and displacement conditions on the boundary of the half space. The analysis holds for the most general anisotropy in which no symmetry elements of the material are assumed.
TL;DR: In this paper, the group theory is solved for molecules of any symmetry matrix isolated at a site in a crystal field of any symmetric matrix, and selection rules are applied to predict spectra in the infrared and Raman effect.
Abstract: The group theory is solved for molecules of any symmetry matrix isolated at a site in a crystal field of any symmetry. As the potential barrier to rotation of the molecule relative to the host crystal is raised, certain symmetry operations become decreasingly ``feasible'' in the sense of Longuet‐Higgins. Using correlation methods the symmetry species of the rotational states are determined from the free rotation limit to any of the librational limits. Examples of linear, symmetric, and spherical rotors are given. From the symmetry of states and the dipole and polarizability tensors, selection rules are applied to predict spectra in the infrared and Raman effect.
TL;DR: An exact MCSCF theory for excited states belonging to the same symmetry species was proposed in this paper, and applied to some of the excited states of the CN radical in the same way as in this paper.
Abstract: An exact MCSCF theory is proposed for excited states belonging to the same symmetry species and is illustrated by actual application to some of the excited states of the CN radical.
TL;DR: In this paper, generalizations of the Thirring model to Fermi fields with U(n) symmetry were treated and scale invariance was maintained only for values of the coupling gv=0 or gv = 4φ(n+1).
TL;DR: In this article, a two-level model is introduced and developed in order to describe the nuclear rotation at high angular momenta, and the implications of this symmetry including various subalgebras of R(8) corresponding to different particular cases are studied.
TL;DR: The total longitudinal force which acts on a high-frequency heated plasma column is derived for any arbitrary absorption mechanism as mentioned in this paper, which results in particle drifts and poloidal fields which may be relevant to toroidal plasma confinement.
Abstract: The total longitudinal force which acts on a high-frequency heated plasma column is derived for any arbitrary absorption mechanism. This force arises from any departure from longitudinal symmetry (longitudinal plasma motion, a single travelling wave, etc.). It results in particle drifts and poloidal fields which may be relevant to toroidal plasma confinement. High-frequency power of order 105 W is sufficient to replace the driving electric field in a moderate scale tokamak.
TL;DR: In this paper, the energies of single-particle states in nuclei with 35 ≦ A ≦ 65 were obtained as eigenvalues of a local Saxon-Woods potential with depth depending linearly on A and on the nuclear symmetry parameter.
TL;DR: The known symmetry of the non-null electromagnetic field, which acts as the source of a four-dimensional space-time satisfying the Einstein-Maxwell equations, is used in this article to show that when such a spacetime admits a group of motions, generated by a Killing vector, the structure constants for the group must satisfy an additional relation to the known relations of group theory.
Abstract: The known symmetry of the non-null electromagnetic field, which acts as the source of a four-dimensional space-time satisfying the Einstein-Maxwell equations, is used to show that when such a space-time admits a group of motions, generated by a Killing vector, the structure constants for the group must satisfy an additional relation to the known relations of group theory.
TL;DR: The elastic fields of line force couples have been shown to be applicable to the description of dislocation core fields and the conventional anisotropic elastic theory of line defects is extended to include such couples.
Abstract: The elastic fields of line‐force couples have been shown to be applicable to the description of dislocation core fields. The conventional anisotropic elastic theory of line defects is extended to include such couples. Explicit results are presented for cases of high‐crystallographic symmetry for which the results can be expressed in simple analytical form.
TL;DR: In this paper, it is shown that if a conservative dynamical system admits a trajectory collineation, then in general a new quadratic (in the velocity) constant of the motion will result from the deformation of a given quadratically constant of motion under such a symmetry mapping.
Abstract: By use of Lie derivatives, symmetry mappings for conservative dynamical systems are formulated in terms of continuous groups of infinitesimal transformations within the configuration space. Such symmetry transformations, called trajectory collineations, may be interpreted as point mappings which drag along coordinates and geometric objects as they map trajectories into trajectories. It is shown that if a conservative dynamical system admits a trajectory collineation, then in general a new quadratic (in the velocity) constant of the motion will result from the deformation of a given quadratic constant of the motion under such a symmetry mapping. The theory is applied to obtain the group of symmetry transformations and concomitant constants of the motion associated with the deformations of the energy integral for the Kepler problem and for the isotropic simple harmonic oscillator. The Runge‐Lenz vector of the Kepler problem and the symmetric tensor constant of the motion for the three‐dimensional oscillator...
TL;DR: In this paper, a rotational diffusion model was proposed to calculate the spin-lattice relaxation time T 1 due to spin-rotation interaction in liquids of symmetrical molecules.
TL;DR: In this article, a method for perturbation of quantum systems with a symmetry is presented. But the method is not suitable for the case of the center-of-mass motion of a nucleus, the symmetry being the translational invariance.
Abstract: For quantum systems with a symmetry it is often convenient to start from a simple soluble model lacking the symmetry, and restore the symmetry by projection. If this is done for all eigenstates of the model system, one obtains an overcomplete set of basis functions, which is not suitable for standard perturbation theory. The paper develops a method by which one can do perturbation theory in this situation. The method is illustrated by application to the problem of the centre-of-mass motion of a nucleus, the symmetry being the translational and Galileo invariance.
TL;DR: In this paper, the application of a simple relationship between atomic orbital integrals and symmetry orbital integral is described in connection with traditional uses of symmetry, and simple modifications for implementation in the POLYATOM molecular self-consistent field programs are given and discussed.
TL;DR: In this paper, it is shown how one can obtain, extending Birman's method, the symmetry of the soft modes in general second order phase transitions which occurs at k≠0 points in Brillouin zone accompanying the primitive cell volume enlargement.
TL;DR: Using the principle of symmetry of the kinetic coefficients, the material equation structure in gyrotropic media with sharp boundaries was determined in this paper, and the obtained results were also valid in the presence of energy losses in the surface layer.
TL;DR: In this paper, the authors derived the symmetrized form of the spectrum equation of the scattered-wave model for molecules in a symmetric form, and proved its correctness.