On the violation of certain conservation laws at critical values of parameters and quasi-catastrophe theory

We describe briefly how quasi-catastrophe theory can explain the phenomena of the violation of certain conservation laws and other spontaneous changes in a given physical system like phase transitions etc.     

Projective differential geometry and geodesic conservation laws in general relativity,II: Conservation laws

We examine the geodesic conservation laws associated with the projective actions discussed in our earlier paper with the same overall title. Using the Cartan formalism, a one-to-one correspondence between a class of these actions and all geodesic conservation laws is possible. In particular there is a natural geometric interpretation of Killing tensors. Homothetic motions are shown to correspond to conserved quantities on all geodesies (not just null ones). The same approach identifies homothetic Killing tensors and a universal quadratic first integral which reduces to the conformai Killing tensor case on null geodesics.     

A CP violating mixing matrix compatible with neutral flavour conservation and spontaneous CP violation

A specific ansatz for the Yukawa couplings of a four-generation SU(2)_L×U(1) model with two Higgs doublets is discussed which leads to neutral flavour conservation, spontaneous CP violation and to a genuinely complex mixing matrix. W exchange conserves CP in the limit m_t′ = m_t only. The decay rate for t→b is reduced by factor two compared to the standard model wit three generations. The phenomenological implications for K⁰−K̄⁰ and B⁰−B̄⁰ are investigated.     

Chiral anomaly in Weyl systems: No violation of classical conservation laws

The anomalous term $～\mathbf{E}\mathbf{B}$ in the balance of the chiral density can be rewritten as quantum current in the classical balance of density. Therefore it does not violate conservation laws as sometimes claimed to be caused by quantum fluctuations.     

Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory I. Nonlocal conservation laws

Nonlocal integral conservation laws in the Einstein-Cartan theory for the energy-momentum tensor of general-form sources, in essence being an integral equivalent of convoluted Bianchi identities, are obtained.     

ADM pseudotensors,conserved quantities and covariant conservation laws in general relativity

The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though not necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitly the range in which standard techniques are equivalent to covariant conserved quantities.The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases.     

Internal symmetries and the conservation laws for the classical theory of a vector field of general type

A study is made of a six-parameter internal-symmetry group of the classical theory of a vector field of general type (and its nonlinear generalizations). This group, which is not related to a change of the space-time coordinates, is interpreted physically.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 77–81, April, 1978.We are sincerely grateful to F. I. Fedorov for interest in the work, and also to A. A. Bogush, L. F. Zhirkov, and E. A. Tolkachev for helpful and critical discussion of our results.     

A unified approach to conservation laws in general relativity,gauge theories,and elementary particle physics

A unified treatment of conservation laws in general relativity, gauge theories, and elementary particle physics is formulated in the setting of principal fiber bundles. The group AUT(P) is introduced as the general gauge transformation group that covers space-time coordinate transformations. A set of master equations is exhibited for any Lagrangian density generally covariant with respect to AUT(P). The symmetry group for elementary particle theory is shown to be the structure group of the bundle only in the special case when the gauge potential is flat and the space-time is simply connected. In the general case, the symmetry group is reduced to the symmetry group of the gauge potential. This natural mechanism for a reduction of the symmetry group is speculated on as a model for spontaneous symmetry breaking.This essay received an honorable mention from the Gravity Research Foundation for the year 1981-Ed.Partially supported by a grant from the National Science Foundation.     

New theory of Lorentz violation from a general principle

We report that a general principle of physical independence of mathematical background manifolds brings a replacement of common derivative operators by co-derivative ones. Then we obtain a new Lagrangian for the ordinary minimal standard model with supplementary terms containing the Lorentz invariance violation information measured by a new matrix, denoted as the Lorentz invariance violation matrix. We thus provide a new fundamental theory to study Lorentz invariance violation effects consistently and systematically.     

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J , L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.     

Field equations and conservation laws in the nonsymmetric gravitational theory

The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an Einstein plus fields theory. From this, it is deduced that the energy is positive in the radiation zone.     

Lorentz violation,quantum tunneling,and information conservation

In this paper, by introducing the Lorentz-invariance-violation(LIV) class of dispersion relations(DR)suppressed by the second power(E/EQG)2, we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordstrom(RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle. However, at the same energy level, it was insensitive to changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation.We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.     

Additive conservation laws in local relativistic quantum field theory

We consider generatorsQ of symmetry transformations acting additively on asymptotic particle states according to (1.1). [This equation can be derived forQ defined as integral over a conserved local current!]. For simplicity, we consider only the case that all asymptotic fields are scalar. Assuming that elastic scattering occurs at least in an open subset of the scattering manifold we show thatQ is at most alinear combination of generators of the Poincaré group and internal symmetries.     

Torsion and conservation laws

The interaction of spinor and electromagnetic fields with the torsion of space-time is studied within the framework of the Einstein-Cartan theory. The equivalent nonlinear theory in Riemann space is obtained. The conservation laws for the vector and pseudovector currents are investigated in the nonlinear theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–52, February, 1986.     

Syzygies and conservation laws

We show how the notion of syzygies of a system of partial differential equations allows to derive some conservation laws, for the case of Maxwell and Proca systems. More in general, we apply some classical tools in algebraic analysis to derive properties of the solutions of the previous systems like their integral representations.     

On Synge's covariant conservation laws for general relativity

Following Synge, the covariant formulas for the total four-momentum and angular momentum of an isolated physical system in general relativity are derived. These formulas are first obtained in the weak-field approximation, for which they are shown to be expressible in surface integral form, to be unique, and to represent covariantly conserved quantities. The covariant expressions for the general case are then shown to be identical to those for the weak-field case. The uniquely determined and covariantly conserved quantities so obtained are found to agree with the corresponding canonical, noncovariant surface integral expressions.     

On the Rayski formulation of the laws of conservation in general relativity

The Rayski method is used to calculate the energy of a static and spherically symmetrical gravitational system.In conclusion, the author thanks Dr. P. Burcev and Dr. K. Kucha for kindly pointing out some shortcomings which could thus be eliminated in time.     

Chemisorption phenomena: Analytic modeling based on perturbation theory and bond-order conservation

Tremendous advances in experimental studies of chemisorption revealed that many phenomena could not be understood and projected by the current theoretical constructs. We discuss some of the experimental puzzles that prompted a development of new analytic approaches to chemisorption based on general principles such as perturbation theory (PT) and bond-order conservation (BOC). The PT results concern the periodic regularities of the heat of chemisorption, the role of the antibonding adsorbate orbitals, and universal patterns of adsorbate-induced surface polarization Some of the PT findings are further corroborated within a much broader BOC approach. The BOC model and its postulates (including the use of a Morse potential) and diverse projections are thoroughly discussed. For atomic A and diatomic AB adsorbates, it is shown how the BOC model explicitly and rigorously interrelates a variety of seemingly disparate phenomena such as preferred adsorbate sites, the activation barriers for surface migration and dissociation, relations between atomic Q_A (Q_B) and molecular Q_AB heats of chemisorption, coverage and coadsorption effects on Q_A, overlayer phase transitions and island formation, the nature of promotion and poisoning. The model also projects possible intermediates and elementary steps of surface reactions. Although some of the findings are counter to commonly held perceptions, the whole picture of chemisorption is coherent and fits experiment well. The new conceptual understanding is stressed and some comments on the theory of chemisorption are made.