Showing papers on "Explicit symmetry breaking published in 1968"
TL;DR: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented in this article, where several kinetic schemes which lead to an unstable behavior are indicated, and the role of diffusion is studied in more detailed way.
Abstract: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented. Several kinetic schemes which lead to an unstable behavior are indicated. The role of diffusion is studied in a more detailed way. Moreover we devote some attention to the problem of occurrence of time order in dissipative systems. It is concluded that there exists now a firm theoretical basis for the understanding of chemical dissipative structures. It may therefore be stated that a theoretical basis also exists for the understanding of structural and functional order in chemical open systems.
1,212 citations
TL;DR: In this paper, it is shown that to produce optical rotation in a chromophore, a potential function must have the symmetry properties of a pseudoscalar in the symmetry group of the unperturbed chromophores.
Abstract: It is shown that to produce optical rotation in a chromophore, a potential function must have the symmetry properties of a pseudoscalar in the symmetry group of the unperturbed chromophore It is thus possible to establish regional rules of optical rotation without recourse to particular models and assumptions of the electronic states of the chromophore Formulas and geometric representations of the resulting regional rules are given for a number of symmetries which are encountered in molecular problems The results are not applicable to coupled oscillator models of optical rotation
354 citations
353 citations
35 citations
21 citations
21 citations
01 Jan 1968
TL;DR: The symmetry of a physical system is because of idealizations, such as closed systems, isotropic spaces, ideal gases, incompressible fluids, and perfect solids as mentioned in this paper.
Abstract: Publisher Summary This chapter discusses stationary states in the quantum theory of matter, group of the Hamiltonian, symmetry groups of solids, lattice vibrations in solids, and band theory of solids. Group theory has become a most useful tool in modern physics for systematizing the description of idealized processes dealing with theoretical concepts such as energy, mass, charge, momentum, and angular momentum; for classifying states in the quantum theory of matter; and further, for simplifying numerical applications of physical laws. The symmetry of a physical system is because of idealizations, such as closed systems, isotropic spaces, ideal gases, incompressible fluids, and perfect solids. Crystal symmetry is an interesting subject for detailed study because of the variety of lattice structures occurring in nature. Considerations of symmetry alone may be the most essential part of the work in determining the properties of crystalline solids. It is necessary to make use of the crystal symmetry in order to be able to obtain numerical solutions for the equations of motion of identical particles, such as electrons, phonons, or photons, moving in perfect solids.
20 citations
20 citations
TL;DR: In this article, the role of time-reversal symmetry in determining the possible forms of macroscopic laws has been clarified, as well as the criteria for the occurrence of spontaneous electric and magnetic moments.
Abstract: In an earlier paper [Amer. J. Phys. 36, 735 (1968)] of the same title one of us described a particularly simple method by which symmetry considerations can be applied to determine the possible forms of macroscopic laws. In this sequel we clarify the role of time-reversal symmetry, describe more fully the criteria for the occurrence of spontaneous electric and magnetic moments, discuss the application of the method to magnetically ordered systems, and correct a number of errors in the tables.
19 citations
TL;DR: In this article, it is shown how symmetry properties of the potential function may be utilized to find normal modes of vibration in a non-linear system with nonlinear equations of motion.
Abstract: Conservative mechanical systems having non-linear equations of motion are considered. It is shown how symmetry properties of the potential function may be utilized to find normal modes of vibration. If the systems consist of space arrays of masses interconnected by springs, and they have certain geometrical symmetries, then these will be reflected in symmetry properties of the potential function. This theory is applied to a number of examples.
15 citations
TL;DR: An explicit derivation of a general property of symmetry of the non-local optical potential is given by using the projection operators in this paper, which in a particular case reduces to the symmetry in the position coordinates, insures the relation of reciprocity and follows from the reversibility of the original multi-channel system.
TL;DR: In this article, a modified form of Weinberg's second sum rule is proposed, and relations among vector-meson masses are obtained on the assumption of nonet symmetry for the currents.
Abstract: It is shown that in gauge-field models for the electromagnetic and weak hadronic currents, restrictions are imposed on the way the symmetry is broken if the algebra of currents is to hold. A modified form of Weinberg's second sum rule is proposed, and relations among vector-meson masses are obtained on the assumption of nonet symmetry for the currents.
TL;DR: In this paper, the general properties of the internal symmetry crossing matrices are derived for an arbitrary compact internal symmetry group and the interpretation of the reduced amplitudes which they relate is discussed.
TL;DR: In this paper, model equations are studied for the purpose of gaining some understanding about the possible origins of strong SU(3)$ breaking, and a class of equations are described for which, amongst others, solutions exist such that they are tilted with respect to the plane defined by the driving forces, thereby generating the formal equivalent of a Cabibbo angle, and large asymmetries occur in a direction which is the one of hypercharge up to electromagnetic corrections.
Abstract: Model equations are studied for the purpose of gaining some understanding about the possible origins of strong $\mathrm{SU}(3)$ breaking. The equations are response equations in the octet space of $\mathrm{SU}(3)$. They have full $\mathrm{SU}(3)$ symmetry apart from electromagnetic and weak driving terms. A class of equations is described for which, amongst others, solutions exist such that (1) they are tilted with respect to the plane defined by the driving forces, thereby generating the formal equivalent of a Cabibbo angle, and (2) large asymmetries occur in a direction which is the one of hypercharge up to electromagnetic corrections.
CERN1
TL;DR: In this paper, a model with a relativistic spinor structure successfully describes meson annihilation processes; large symmetry breaking according to an essentially arbitrary prescription is required to obtain these results using the usual model.
TL;DR: In this paper, the symmetry properties of an n-electron correlation function are determined by those of the spin-orbital products which they replace in Ψ0, and this is not in general true for an open-shell state.
Abstract: The resolution of a correlated wave function Ψ about an orbital approximation Ψ0 for any state of an N-electron system is discussed with particular reference to the symmetry conditions which the n-electron correlation functions of Xn must satisfy in order that Ψ have the correct symmetry properties for the state in question. It is shown how for a closed-shell state the symmetry properties of the correlation functions are determined by those of the spin-orbital products which they replace in Ψ0, and how this is not in general true for an open-shell state. It is shown how the symmetry properties of an n-electron correlation function can always be uniquely defined by those of the (N-n)-electron spin-orbital product to which it is coupled in Xn , and the general symmetry conditions which the correlation functions must satisfy are derived.
TL;DR: In this article, it was shown that the PY and HNC integral equations are not symmetric with respect to the permutation of the particles in a pair distribution function, and that they do not satisfy the symmetry condition for any self consistent approximation.
Abstract: The functional formalism described in a preceding paper, leads to a great number of integral equations for molecular distribution functions. Some of them have a certain symmetry property which, in the case of the pair distribution function includes symmetry with respect to the permutation of particles. This symmetry condition is necessary for any self consistent approximation. Among all integral equations known to date only the PY and the HNC equations satisfy this condition. In this paper we derive some new symmetric equations. Integral equations which are obtained with the help of the Percus method, involvingn-particle distribution functions (n > 2), cannot be symmetric with respect to the interchange of particles.
[...]
TL;DR: In this paper, the SU3 breaking in the effective coupling constants for a vector meson decaying into two ps mesons is discussed from the point of view of a Lagrangian field theory of vector mesons, essentially based on the Ward identity and the Johnson sum rule.
Abstract: TheSU3 breaking in the effective coupling constants for a vector meson decaying into two ps mesons is discussed from the point of view of a Lagrangian field theory of vector mesons, essentially based on the Ward identity and the Johnson sum rule. With reasonable approximations, the results of current algebra or of sum rules for the spectral functions ofSU3 symmetry are reproduced, although the dynamical assumption on the symmetry breaking is not the same.