Conservation laws in general relativity

In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.The authors would like to thank Dr. P. Burcev from the Dept of Theoretical Physics, J. E. Purkyn University in Brno, and Dr. K. Kucha from the Dept. of Theoretical Physics, Charles University in Prague, for their permanent interest in this work and for valuable discussions.     

Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Conservation laws for cosmological perturbations

We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution given by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de Sitter geometry as background. We relate the obtained conserved quantities to Traschen's integral constraints and mention a few applications in cosmology.     

Conservation laws in asymptotically separable quantum mechanics

A notion of chronological disorder is introduced to explain the physical reason why many familiar conservation laws should not be regarded as sacrosanct and valid for all times. Their disappearance as absolute laws in an asymptotically separable theory is a desirable feature, rather than a difficulty, of the theory.     

Conservation laws and residual interaction in nuclei

Zeitschrift für Physik A Hadrons and nuclei - We discuss relations between single-particle energies and parameters of the residual interaction in nuclei, which follow from galilean and gauge...     

Conservation laws in a directed sandpile model

We derive a complete set of conservation laws for a directed sandpile model originally studied by Dhar and Ramaswamy, and discuss the rather minimal effect of these laws on the dynamics of avalanches.     

Conservation laws for polynomial quantum Hamiltonians

A construction method for the conservation laws for a broad class of polynomial quantum Hamiltonians is proposed. Also the classification of irreducible representations of some nonlinear commutation relation is given.     

Conservation laws in General Relativity in the Vierbein formalism

Conservation laws for dynamical systems in Riemannian space-time in the Vierbein formalism are deduced from the existence of motions in the space-time. The result is applied to Dirac's equation in General Relativity. Research partially supported by the National Research Council of Canada.     

Conservation laws in stochastic deposition-evaporation models in one dimension

An infinite number of conservation laws is identified for a stochastic model of deposition and evaporation of trimers on a linear chain. These laws can be encoded into a single nonlocal invariant, the irreducible string, which uniquely lables an exponentially large number of kinetically disconnected sectors of phase space. This enables the number and sizes of sectors to be determined. The effects of conservation laws on some thermodynamic properties are studied.     

Conservation laws of free Klein Gordon fields

It is proved that the free Klein Gordon fields of spatial dimension 2 have no conservation laws expressible by differential polynomials with constant coefficients other than those found by Kibble [5].Partially supported by Sakkokai Foundation and the National Science Foundation.     

Conservation laws and the electric Aharonov-Bohm effect

The original derivation of the electric Aharonov-Bohm effect is analysed. It is shown that the operation of a simple device based upon the principles used in that derivation is incompatible with the law of energy conservation. It is concluded that the original proof of the effect is incorrect.     

Conservation laws derived by the Neutral-Action Method

Conservation laws are a recognized tool in physical- and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schr?dinger equation is presented.