Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

Proton dipolar spin-lattice relaxation in hexagonal ice

The ultraslow motion of defects in high purity hexagonal H₂O ice has been studied by proton dipolarT _1D measurements in the strong collision limit, using the Jeener technique. The obtained NMR correlation times agree rather well with both the Schottky H₂O diffusion timest _s=r ²/6D and the deuteron correlation times in D₂O ice, suggesting that Schottky rather than interstitial diffusion dominates spin-lattice relaxation in both H₂O and D₂O ice.On leave of absence from University of Ljubljana, Institute J. Stefan.     

On Poisson brackets and symplectic structures for the classical and quantum zitterbewegung

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x ,p ,v ,S ^v). The only difference is in the normalization of the Dirac velocities =4 which has significant consequences.Dedicated to David Hestenes, whose work profoundly connects geometry (spacetime), algebra (Clifford), and physics (electron).     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

Proof of confinement of static quarks in 3-dimensionalU(1) lattice gauge theory for all values of the coupling constant

We study the 3-dimensional pureU(1) lattice gauge theory with Villain action which is related to the 3-dimensional -ferromagnet by an exact duality transformation (and also to a Coulomb system). We show that its string tension is nonzero for all values of the coupling constantg ², and obeys a bound const·m _D^–1 for smallag ², with =4²/g ² and . A continuum limita0,m _D fixed, exists and represents a scalar free field theory of massm _D. The string tension m _D ^–2 in physical units tends to in this limit. Characteristic differences in the behaviour of the model for large and small coupling constantag ² are found. Renormalization group aspects are discussed.Work supported in part by Deutsche Forschungsgemeinschaft     

An estimation of the fine structure constant using fiber bundles

We calculateg ₀/e whereg ₀ is the strength of an elementary magnetic monopole ande the charge on the electron, in terms of a ratio of loop sizes in the twisted and untwisted principal fiber bundles withU(1) the structure group andR ³-{0} the base space. The result involves the present distance around theU(1) space and, rather surprisingly, the structure of the quantum gravitational vacuum. Combining our result with the expression foreg ₀ from the Dirac quantization condition gives a final estimate for the fine structure constant,1/100.     

Ruby ESR Over a Wide Frequency Range in the Millimeter Wave Region

The ESR of Cr³⁺ in dark ruby is measured using a high frequency ESR spectrometer with a wide frequency range which uses a gyrotron as the radiation source. For this purpose, GYROTRON FU- IV A developed at Fukui University was optimized for use in an ESR apparatus operating in the millimeter-wave range.The observed fine structure constant D for ruby is found to be D –5.728 GHz and the g-values g 1.981, g 1.982. Both the values of |D| and g are smaller than those obtained at lower frequencies by other work. Higher order terms of the spin hamiltonian are discussed in order to understand the ruby ESR results in this higher frequency range.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

830 nm emission in sodium vapor

We demonstrate that the intriguing 830 nm coherent emission, which is observed when sodium vapor is pumped with a high-power pulsed laser tuned near the 3S4D two-photon transition, is due to an axially phase-matched six-wave mixing process. This conclusion is based upon the observation of emission near 584 nm, which is coupled to the 830 nm emission in the six-wave mixing process: ₁+₂=2_L–_4D4P –_4P3D . In addition, we have observed coherent emission near 1.16 m, which is due to an analogous process involving cascade through the 4S (as opposed to the 3D) state. We calculate the wavelengths of all photons involved in these processes using the standard formulas of parametric wave-mixing theory, and show that they can be predicted to within experimental uncertainties. Finally we report observations of significant blue shifts of the 830 nm and 1.16 m emissions in a mixed sodium-potassium vapor. These shifts can be readily understood by considering the effect of the potassium on the frequency-dependent refractive index of the vapor. Due to these results, other recent interpretations of the 830 nm emission as stimulated excimer emission on the Na₂ 1³ _g ⁺ 1³ _u ⁺ band must now be rejected.     

Coordinate-dependent 3 + 1 formulation of the general relativity field equations

This paper presents a coordinate-dependent 3+ 1 decomposition of the general relativity field equations in terms of a scalar potentialc ²[(–g ₄₄)^1/2–1], a vector potentialA _icg _4i/(–g₄₄)^1/2, and the three-space metric _ijg _ij–g_4i g _4j/g ₄₄. The equations are exact and the form of the decomposed equations is valid in any coordinate system.     

Zeta functions and transfer operators for piecewise monotone transformations

Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function (z) of (T, g) extends meromorphically to {z<^-1} (where =lim g^°T^n-1...g^°Tg ^1/n ) and thatz is a pole of if and only ifz ^–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse     

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of d-dimensional Anderson models on l²( $$\mathbb(z)$$^d) defined by the product U=D S where S is a deterministic unitary and D is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of U(U –z)^–1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for U.     

On the correlation for Kac-like models in the convex case

The aim of this paper is to stu the behavior asm tends to of a family of measures exp[- ^(m)(x)]dx ^(m) on ^m , where ^(m) is a potential on ^m which is a perturbation in a suitable sense of the harmonic potential _j x _j ² .     

Fermion masses

In this paper, we show that 2m _e m /(m _e ² +m ² = (g _V/g _A) _e ² . From this expression, the Weinberg mixing parameter is shown to be 0·2254 or 0·2746. Assuming that the electron and muon neutrino masses are degenerate, we find thatm _v = (g _V/g _A) _e ² . (m _e m )/M _WL, where M_WL is the mass of the standard W^± boson. The neutrino mass turns out to be 6·5 eV. The -neutrino mass is found to be about 81 MeV. The masses of c, t, s and b quarks are found to be respectively 1·7 GeV, 21·2 GeV, 0·57 GeV and 2·18 GeV by assumingm _d=m _u= 0·3 GeV. All these masses agree with other estimates except the b quark which has about half of its expected value.     

Determination of the surface tension at the boundary of solid phases

The results are given of an experimental investigation of the kinetics of isothermal coalescence of disperse phases in AI-Mg alloy and in vanadium steel. A method is described of processing the kinetic curves to evaluate the magnitude of the specific surface energy () at the boundary of the solid phases. The reasonableness of the values of obtained atthe boundary-Al-- phase (Al₃Mg₂) and -Fe-cementite (Fe₃C) confirms our calculation of the solubility of the disperse phase.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 114–120, April, 1972.     

Interaction theory: Relativistic hydrogen atom and the Lamb shift

The Dirac relativistic equation for the hydrogen atom as augmented by dual interaction terms is solved exactly and the eigenvalues for the bound states are determined. These areE _n =[1 + ²/ (n + s)²]^–1/2, withs ²=k ²– ²(1±)², where is a constant which is a measure of the strength of the dual interaction relative to the standard interaction ^µ A _µ . It is shown that the ratios of the experimental values for the Lamb shifts of various energy levels in hydrogen and singly ionized helium are correctly given by the theory. The origin of the anomalous magnetic moment and, in fact, the operator for the total magnetic moment is given.     

Excitation functions of the analyzing power in elastic proton-proton scattering from 0.45 to 2.5 GeV

Excitation functions A_N(p_lab,_c.m.) of the analyzing power in elastic proton-proton scattering have been measured in an internal target experiment at the Cooler Synchrotron COSY with an unpolarized proton beam and a polarized atomic hydrogen target. Data were taken continuously during the acceleration and deceleration for proton kinetic energies T_lab (momenta p_lab) between 0.45 and 2.5 GeV (1.0 and 3.3 GeV/c) and scattering angles 30 ^° _c.m. 90^°. The results provide excitation functions and angular distributions of high precision and internal consistency. The data can be used as calibration standard between 0.45 and 2.5 GeV. They have significant impact on phase shift solutions, in particular on the spin triplet phase shifts between 1.0 and 1.8 GeV.     

Generalization of the Dirac equation admitting isospin and color symmetries

One possible generalization of the Dirac square root procedure =D _d ^k D _d is presented, based on the explicit introduction of chiral symmetry, which generates a set {d} of symmetry-constrained Dirac fieldsD _{d d} =0admitting isospin and color. A self-consistent discussion is given of the basic geometrical construction, the field equations, and their relationship to chiral symmetry, isospin, and color, and of the construction of the Lagrangian, including the interaction gauge fields. The correspondence of the theory with the standardSU _c(3) ×SU _w(2) ×U _y(1) formulation for quarks and leptons is shown.     

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.     

Scaling functions of susceptibilities toO(1/n) forn-vector models with axial anisotropy

For an axially anisotropicn-vector model withm = O(n) easy – andn – m = O(n) hard components of the order parameter, we derive the susceptibility r ^–1 along one of the equivalent easy axes and the perpendicular one r ^-1 toO(1/n) of the 1/n-expansion in the disordered phase. The results confirm predictions of the scaling theory, e.g.(g, t)=A t ^– X (B g/t ) and (g, t) =A t ^– X (B g/t ), wheret = T – T _c (g = 0),g is the anisotropy parameter andX, X denote the scaling functions. We evaluate the relevant diagrams toO(1/n) which yield the coefficientsA, A and the critical behaviour of the scaling functions and critical amplitudes explicitly for . The extreme anisotropic case, i.e.m = O(1), is discussed briefly in the large-n limit in comparison with the mean field solution.Parts of this paper were presented at the Frühjahrstagung der Deutschen Physikalischen Gesellschaft in Freudenstadt (May 1974).