Showing papers on "Conservation law published in 1969"
88 citations
01 Jan 1969
TL;DR: In this article, a variant of the theory of non-conservation of parity is introduced without assuming asymmetry of space with respect to inversion, and various possible consequences of such a theory pertain to the properties of the neutrino are considered.
Abstract: A variant of the theory is proposed in which non-conservation of parity can be introduced without assuming asymmetry of space with respect to inversion.
Various possible consequences of non-conservation of parity are considered which pertain to the properties of the neutrino and in this connection some processes involving neutrinos are examined on the assumption that the neutrino mass is exactly zero.
80 citations
TL;DR: In this paper, the exact conservation laws of general relativity, expressed in terms of the symmetric energy-momentum complex of Landau and Lifshitz, were used to determine the various conserved quantities in the different post-Newtonian approximations.
Abstract: It is shown how the exact conservation laws of general relativity, expressed in terms of the symmetric energy-momentum complex of Landau and Lifshitz, can be used to determine the various conserved quantities in the different post-Newtonian approximations. Particular attention is given to the conserved energy which emerges as the integral over the whole of space of the difference between the (O,O)-component of the Landau-Lifshitz complex and the energy of the conserved mass present. The method is illustrated in the framework of the first post-Newtonian equa.tions of hydrodynamics.
80 citations
TL;DR: In this article, the authors assume that the initial data satisfies a certain order condition which was introduced in [11] and which was also used in [7] to obtain existence theorems.
Abstract: for all smooth functions q~ = q~ (t, x) having compact support. In order to obtain an existence theorem for the problem (1.1), (1.2), we shall assume that the initial data satisfies a certain order condition which was introduced in [11] and which was also used in [7] to obtain existence theorems. Briefly, this condition states that certain initial data gives rise to a specific form of Riemann problem. Thus, if we let (us, vi)=(Uo (x~), v o (x~)), i = 1, 2, for xl 0, is solvable by a shock wave of one
80 citations
32 citations
TL;DR: In this article, the exact solution to the kinetic equation for resonant three wave coupling in weakly turbulent plasmas, assuming only a single triplet of modes interaction is given.
Abstract: Exact solution to kinetic equation for resonant three wave coupling in weakly turbulent plasmas, assuming only single triplet of modes interaction
23 citations
TL;DR: In this paper, it was shown that for any Lagrangian, which is a function of the particle positions and velocities alone, and which is invariant under the infinitestimal time and space translations, it is possible to find an additional exact invariance under a three-parameter set of infinitesimal transformations (which, in general, depends on a functional rather than a function).
Abstract: In Newtonian mechanics the ten classical integrals of the equations of motion of a system of interacting point particles can be related to the invariance of the corresponding Lagrangian under the ten infinitesimal transformations of the Galilei group. Systems described by approximately relativistic equations [such as the Darwin equations in special relativity and the Einstein-Infeld-Hoffmann (EIH) equations in general relativity] also possess ten integrals of equivalent physical significance; previous work has established similar relations with invariance properties of the Lagrangian for only seven of these, but not for the three expressing the uniform motion of the center of mass. It is shown here that for any Lagrangian whatever which is a function of the particle positions and velocities alone, and which is invariant under the infinitestimal time and space translations, it is possible to find an additional exact invariance under a three-parameter set of infinitesimal transformations (which, in general, depends on a functional rather than a function). The transformations define a velocity which for approximately relativistic systems can be interpreted as that of their center of mass; for such systems the three conservation laws following from this transformation express the constancy of this velocity. A number of examples are given; for the Darwin and EIH equations, the conservation laws agree with those previously obtained directly from these equations.
23 citations
21 citations
TL;DR: In this paper, the general projection technique for getting translationally-invariant configuration-space four-particle states of arbitrary symmetry and total orbital angular momentum, out of harmonic-oscillator states in the single relative coordinates was determined.
17 citations
TL;DR: In this paper, Cimento et al. derived the field equations from a variational principle for the usual Lagrangian density ψ(−iγμ∂μ+m) under a certain restriction.
Abstract: The formal structure and the free‐particle solutions of the field equations (Sμνpν + mγμ)ψ = pμψ, derived recently by the author [Nuovo Cimento 51A, 864 (1967)] for realizations of the inhomogeneous de Sitter group are discussed. The enveloping algebra of the group is developed, and the covariance of the field equations under the five‐dimensional rotations C, P, and T is proved. Bhabha's representation of the matrices γμ is completed. Observables, expectation, values and the scalar product are defined, and classical conservation laws are derived. The field equations are derived from a variational principle for the usual Lagrangian density ψ(−iγμ∂μ+m)ψ under a certain restriction. The free‐particle solutions of the field equations are obtained in the canonical and the extreme relativistic representations. The connections between the wavefunctions in these representations, and also in the Foldy‐Wouthuysen representation, are derived.
TL;DR: In this paper, the authors deduced the Lorentz-Dirac-wheeler-Feynman-Rohrlich equation of motion of a charged particle by considering a special case of the Sommerfeld, Markoff, Bohm-Weinstein and Shih-Prastein-Erber equations of motion.
Abstract: In this article we deduce the Lorentz-Dirac-Wheeler-Feynman-Rohrlich equation of motion of a charged particle by considering a special case of the Sommerfeld, Markoff, Bohm-Weinstein and Shih-Prastein-Erber equations of motion. We can prove or classical examples that 1) there is conservation of energy in the Lorentz-Dirac-Wheeler-Feynman-Rohrlich electrodynamics for the «good solution» of these theories and time-dependent (one-dimensional) forces; 2) there appears a theoretical «paradox» for the constant homogeneous magnetic field. Here the total radiation is bigger than the initial kinetic energy! Here there is no conservation of the total observable energies.
TL;DR: In this article, the time evolution of wave correlations (cumulants) in a uniformly turbulent ensemble of weakly nonlinear, dispersive systems is discussed and a kinetic equation for the spectral energy density of the waves is derived in situations where the resonant three-wave decay condition cannot be satisfied.
Abstract: The time evolution of wave correlations (cumulants) in a uniformly turbulent ensemble of weakly nonlinear, dispersive systems is discussed. With closure of the hierarchy for wave correlations appropriate to the inclusion of resonant four‐wave processes, a kinetic equation for the spectral energy density of the waves is derived in situations where the resonant three‐wave decay condition cannot be satisfied. The resulting kinetic equation is a nonlinear integrodifferential equation with driving terms trilinear in the energy density. Some general properties of this equation are discussed including associated conservation relations and the law of increase of entropy.
TL;DR: In this article, Green's theorem is used to obtain the Newman−Penrose constants in flat and asymptotically flat space-time and investigate the invariant transformations which these quantities generate.
Abstract: Green's theorem is used to obtain the Newman‐Penrose constants in flat and asymptotically flat space‐time and to investigate the invariant transformations which these quantities generate. The zero‐rest‐mass free fields and the coupled Einstein‐Maxwell fields are considered and the relationship of this approach to Noether's theorems is discussed.
TL;DR: In this article, the authors discuss relations between single-particle energies and parameters of the residual interaction in nuclei, which follow from galilean and gauge invariance, and give restrictions for the exchange coefficients in a phenomenological interaction and for some interaction parameters of Fermi liquid theory.
Abstract: We discuss relations between single-particle energies and parameters of the residual interaction in nuclei, which follow from galilean and gauge invariance. Restrictions are given for the exchange coefficients in a phenomenological interaction and for some interaction parameters of the Fermi liquid theory.
TL;DR: In this paper, an investigation has been made on the conservation of the muonic lepton number by using a pure neutrino beam and by measuring the charge ratio of the Muons in neutrinos in interactions.
TL;DR: In this article, the classical spin particle was realized by a non-complanar threeleg which is orthogonal to the particles worldline, and the canonical formalism for the affine rotator was developed in some detail.
Abstract: The classical spin particle formerly described by a pole-dipole-like mass distribution is kinematicly realized by a non-complanar threeleg which is orthogonal to the particles worldline. Only twelve of the ten conservation laws following from LORENTZ-invariance and the nine conservation laws following from invariance against arbitrary affine leg transformations are linearly independent, corresponding to the particles twelve degrees of freedom. The interaction of the mass distribution with a weak gravitational field is introduced via the energy-momentum conservation laws, and for the affine rotator the interaction is introduced by means of an appropriate Lagrangian, the two descriptions being equivalent. The canonical formalism for the affine rotator is developed in some detail.
TL;DR: In this article, a matrix formulation of electromagnetic field equations and non-linear conservation laws is given for measurable quantities, and a generalized interference law is derived and its connection with well-known interference laws is shown.
Abstract: In this paper a matrix formulation of electromagnetic field equations and non-linear conservation laws is given for measurable quantities. In the first part a correlation matrix K is defined for non-stationary fields and the equations and non-linear conservation laws are derived for this matrix. In the second part a transition to the stationary field is performed. Equations of the free field are solved and a generalized propagation law for the correlation matrix K is obtained. Further, a generalized interference law is derived and its connection with well-known interference laws is shown.
TL;DR: In this article, the autocorrelation function for the quasi-momentum density is derived and the transport equation for it is similar in structure to the phonon Boltzmann equation.
Abstract: Non-equilibrium phenomena in crystal lattices determined by the long-time behaviour of the system are formulated in terms of the correlation function of quantities relaxing very slowly, such as the densities of the conserved variables in the system. Transport equations for such correlation functions can be derived and, depending explicitly on the conservation laws of the system, facilitate an analytic solution of the problem. As an example, we examine the autocorrelation function for the quasi-momentum density. The transport equation for it is similar in structure to the phonon Boltzmann equation with a modification of the collision term describing the relaxation of the quasi-momentum density rather than of the phonon density.
TL;DR: In this paper, the cone bands theorem is proved for a classical field theory model and a tensor reduction procedure on conserved and asymptotically conserved quantities is defined.
TL;DR: In this article, the conservation of the nucleus current considering it to be of one-particle structure is discussed, and the effect of this conservation on the structure of the nuclei is discussed.
TL;DR: In this article, it is argued that the total number of fermions, parafermions and quasi-parabosons is absolutely conserved modulo 2 in all reactions.
TL;DR: In this paper, the second-order classical coherence theory of the electromagnetic field in the presence of random sources is presented, and the dynamics of the secondorder correlation tensors may be reduced to a simpler form in terms of certain tensor potentials.
Abstract: Relativistic formulation is presented of the second-order classical coherence theory of the electromagnetic field in the presence of random sources. It is shown that the dynamics of the second-order correlation tensors may be reduced to a simpler form in terms of certain tensor potentials. The gauge transformations of these tensor potentials are considered. In particular, two gauges of special interest are found, analogous to the Lorentz gauge and the radiation gauge in Maxwell’s electromagnetic theory. Some interesting relations and conservation laws are presented.