A relation between local and total energy in general relativity

For a large class ofN-body potentialsV we prove that if is an eigenfunction of –+V with eigenvalueE then sup{²+E:0, exp(|x|)L ²} is either a threshold or +. Consequences of this result are the absence of positive eigenvalues and optimalL ²-exponential lower bounds.Research in partial fulfillment of the requirements for a Ph.D. degree at the University of VirginiaPartially supported by U.S. — N.S.F. grant MCS-81-01665     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Double hypernuclei and the Λ-Λ interaction

The binding energy of the double hypernucleus Be¹⁰ analyzed using an -particle model. A relationship is found between B, the binding energy of two -particlcs, and ¯V, the - potential integral. For the experimental value B = 17.5 Me V ¯V varies from 250 to 850 MeV-F³ according to the form of the - potential used.In conclusion, I wish to thank S. N. Kryuchkova for carrying out these calculations on a Minsk-2 electronic computer. I also wish to thank my senior colleague, V. A. Filimonov, for his support in the completion of the present work.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

A new approach to the problem of the anomalous magnetic moment of the electron

A heuristic model for deriving the anomalous magnetic moment of the electron is presented. A term /2 – 0.327(/)² is deduced, in better agreement with experiment than is the QED derivation of /2 – 0.328(/)². The result is strengthened by the recent non-QED account of the Lamb shift by Yu and Sachs.     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

The strength of Einstein's equations

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC , = 0 whereC is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.     

Quadratic lagrangians in a space with torsion and the theory of the spinor gauge field

The linear approximation of the theory of the spinor gauge field (TSGF), introduced in the localization of the group of tetrad Lorentz transformations, is discussed. In constructing the TSGF, use is made of the principle of correspondence with the tetrad theory of gravitation in a space of absolute parallelism. It is shown that the imposing of additional conditions of the Lorentz-Hilbert type in the linearized TSGF leads to a unique definition of the Lagrangian of the A-field, quadratic in the field intensity, of the form RR. which is usually postulated from considerations of simplicity and by analogy with other gauge fields. Two new identities in a space with torsion are proved.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 74–79, September, 1979.     

Multifractality and scaling in disordered mesoscopic systems

We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, thef() spectrum. The analysis off() spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then thef() spectra of normalized scaling variables must be universal. The critical exponentv of the correlation length is determined by the value (0) wheref() takes its maximum and the scaling exponent of normalizationxv ^–1=(0)+x. As an illustrative example we calculate numerically thef() spectra of eigenstates in the critical regime of 2d disordered electron systems in high magnetic fields. We find similarf() spectra indicating universal log-normal distributions of scaling variables.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Calculation of hyperfine interactions measured by magnetic decoupling in oxygen ions

Magnetic hyperfine interactions in highly stripped oxygen ions recoiling in vacuum have been measured with perturbed angular correlations. The second excited state of¹⁶O(I =3^–,E _X=6.13 MeV, =26.6 psec, |g|=0.55) was produced with the nuclear reactions¹⁹F(p,)¹⁶O and¹⁶O(,)¹⁶O and the angular correlation of the -rays observed in coincidence with particles emitted at 180°. Five recoil velocities between 1.0 and 3.3% c produced average ion charge states from 2.1 to 5.5. The perturbation of the angular correlation and hence the decoupling of the hyperfine interactions was observed as a function of an external axial magnetic field varied between 0 and 33 kG. The perturbation is expected to arise primarily from hyperfine interactions of unpaired 1s electrons with smaller contributions from 2s electrons and other configurations. The maximum external field was strong enough to decouple all hyperfine interactions except that of the 1s electrons. The decoupling curves obtained were successfully fitted by calculations using the hyperfine interactions of the pertinent atomic Hartree-Fock-Slater orbitals.Supported in part by the National Science Foundation.     

The energy-momentum gravitational pseudotensor and Kerr-Schild metrics

It is shown that the Landau-Lifshitz pseudotensor vanishes for any Kerr-Schild metricg =n + 2Hl l satisfying the conditionS l =0. Some solutions verifying this condition are indicated.     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Mössbauer spectroscopy study on the hydrothermal transformation α-FeOOH→α-Fe2O3

The reaction kinetics of the hydrothermal transformation -FeOOH-Fe₂O₃ was studied by means of Mössbauer spectroscopy. From the reaction isotherms, a monomolecular, first order reaction was found to characterise the hydrothermal transformation of alpha oxihydroxide to the alpha iron oxide. The rate constant as well as the activation energy of this process were determined. No intermediate phases were identified in the hydrothermal samples. The thermodynamic properties of the hydrothermal system -FeOOH-Fe₂O₃ in correlation with Mössbauer spectroscopy data are discussed.     

Measurements of 110Xe and 106Te decay half-lives

The -decays of ¹¹⁰Xe and ¹⁰⁶Te were studied at the GSI on-line mass separator. By using the grow-in and decay of the activity, observed in pulsed-beam measurement, the half-life of ¹¹⁰Xe was found to be T_1/2 = 105⁺³⁵_-25ms. The lifetime of ¹⁰⁶Te was determined to be T_1/2 = 70⁺²⁰_-10s by measuring the time between two successive ¹¹⁰Xe ^{106} Te ^{102} Sn -decays. The newly determined half-lives were used to calculate reduced -decay widths for ¹⁰⁶Te and ¹¹⁰Xe. Universal systematics of reduced widths are proposed to search for the evidence of enhancement of the formation amplitude in the emitters above ¹⁰⁰Sn.     

Quasi-stationary states of hydrogen

We consider the hydrogen atom within the context of a theory of relativistic quantum mechanics that allows for a probabilistic interpretation of the wave function. We find the radial equation that determines the energy levels of bound states, represented by quasi-stationary states. We compute the order of magnitude of the shifts from the usual spectrum obtained from the Dirac equation, and we find that the leading terms for these corrections are of the order of ⁶ log fors-states and ⁶ for other states. They are small compared to the Lamb shift, which is of the order of ⁵ log .     

Boundary Effects on Exact Solutions of the Lagrangian-Averaged Navier–Stokes-α Equations

In order to clarify the behavior of solutions of the Lagrangian-averaged Navier–Stokes- (LANS-) equations in the presence of solid walls, we identify a variety of exact solutions of the full equations and their boundary layer approximations. The solutions demonstrate that boundary conditions suggested for the LANS- equations in the literature⁽¹⁾ for a bounded domain do not apply in a semi-infinite domain. The convergence to solutions of the Navier–Stokes equations as 0 is elucidated for infinite-energy solutions in a semi-infinite domain, and non-uniqueness of these solutions is discussed. We also study the boundary layer approximation of LANS- equations, denoted the Prandtl- equations, and report solutions for turbulent jets and wakes. Our version of the Prandtl- equations includes an extra term necessary to conserve linear momentum and corrects an earlier result of Cheskidov.⁽²⁾