Space-time microstructure and singularity-free quantum field theory

It is shown that the dynamical consistency requirements of quantum field theory and the Lorentz-invariant character of particle kinematics and wave equations are compatible with the postulate that physical space is a complex manifold with Euclidean-Gaussian measure in the small. Such a postulate for the microstructure of space introduces a fundamental length(10^–16 cm) and leads to-functions that are analytic on the light-cone for a free field, and hence to self-energies and renormaiization constants that are finite for interacting fields.Work supported by a National Science Foundation grant.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

Parton distributions for high energy collisions

Recent data from deep inelastic scattering experiments atx10^–2 are used to fix the parton distributions down tox10^–4 andQ ²0.3 GeV². The predicted extrapolations are uniquely determined by the requirement of avalence-like structure ofall parton distributions at some low resolution scale and are furthermore shown to be insensitive in the small-x region, 10^–4x10^–2, to the detailed experimental input at the presently accessiblex>10^–2. Simple parameterizations of the resulting parton distributions are presented in the range 10^–5x<1 and=">Q ²10⁸ GeV² as obtained from the leading- and higher-order evolution equations.     

A new test of the weak equivalence principle

The Eötvös, Dicke, and Braginski experiments do not rule out the recent suggestion that the weak equivalence principle (WEP) might be violated at intermediate ranges (10^–1 m r 10⁴ m). I briefly discuss the problems inherent in Eötvös-type apparatus in searches for WEP-violating forces (hyperforces) between laboratory masses and suggest an alternative detector free of such problems. The proposed detector is driven by a hyperforce torque at the rotational frequency. If the detector is tuned to this frequency, the signal, enhanced by resonance, may be detected synchronously. I derive the response equations for the detector and discuss how spurious responses due to gravity torques may be suppressed.This essay received the third award from the Gravity Research Foundation for the year 1986-Ed.     

Quantum space-time and gravitational consequences

Relativistic particle dynamics and basic physical quantities for the general theory of gravity are reconstructed from a quantum space-time point of view. An additional force caused by quantum space-time appears in the equation of particle motion, giving rise to a reformulation of the equivalence principle up to values ofO(L ²), whereL is the fundamental length. It turns out that quantum space-time leads to quantization of gravity, i.e., the metric tensorg _v () becomes operator-valued and is not commutative at different pointsx andy in usual space-time on a large scale, and its commutator depending on the vielbein field (gaugelike graviton field) is proportional toL ² multiplied by a translation-invariant wave function propagated between pointsx andy . In the given scheme, there appears to be an antigravitational effect in the motion of a particle in the gravitational force. This effect depends on the value of particle mass; when a particle is heavy its free-fall time is long compared to that for a light-weight particle. The problem of the change of time scale and the anisotropy of inertia are discussed. From experimental data from testing of the latter effect it follows thatL10^–22cm.     

Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.     

Tensor analysis and curvature in quantum space-time

Introducing quantum space-time into physics by means of the transformation language of noncommuting coordinates gives a simple scheme of generalizing the tensor analysis. The general covariance principle for the quantum space-time case is discussed, within which one can obtain the covariant structure of basic tensor quantities and the motion equation for a particle in a gravitational field. Definitions of covariant derivatives and curvature are also generalized in the given case. It turns out that the covariant structure of the Riemann-Christoffel curvature tensor is not preserved in quantum space-time. However, if the curvature tensor _v (z) is redetermined up to the value of theL ² term, then its covariant structure is achieved, and it, in turn, allows us to reconstruct the Einstein equation in quantum space-time.     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.     

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae ^{2 p} (1+a ₁ e ^– + ...) as , with p1. The staggered susceptibility behaves as _stagg ^5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

All torsion-free spherical vacuum solutions of the quadratic Poincaré gauge theory of gravity

We find all torsion-free, spherically symmetric, vacuum solutions to the theory of gravity recently proposed by Hehl, Ne'eman, Nitsch, and von der Heyde. There are three classes of solutions: (A) the Schwarzschild metrics with arbitrary mass,M, and arbitrary cosmological constant, ; (B) the Nariai-Bertotti metrics with arbitrary positive cosmological constant, ; and (C) the conformally flat metrics whose conformai factor is ²/ ² where is a function of only the time coordinate , and the radial coordinate, and satisfies the wave equation in these variables. Hence there is no Birkhoff theorem for this theory. In fact, solutions (C) include some asymptotically flat but nonstationary solutions. On the other hand, solutions (A) include a gravitational confinement potential, as was sought by Hehl et al., since when <0, the weak field limit of the Schwarzschild metric becomes a harmonic oscillator potential. We also discuss the relationship of this theory to the Eddington theory, the Lichnerowicz-Kilmister-Newman-Yang theory, the Nordström theory and the Einstein theory with a cosmological constant.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Angular dependence of the superexchange interaction Fe3+-O2−-Cr3+

The super-exchange interaction parametersI(Fe, Cr) of Fe³⁺ and Cr³⁺ in iron doped rate-earth orthochromitesRCr_0.99Fe_0.01 O₃ (R=La, La_0.5Nd_0.5, Nd, Sm, Gd, Dy, Y, Er, Yb or Lu) have been obtained from⁵⁷Fe magnetic hyperfine structure measurementsvia the Mössbauer effect.The dependence of the experimental valuesI(Fe, Cr) on the Fe–O–Cr average superexchange angle (depending upon the relative size of the rare-earth (RE) ionR ³⁺) is well described by the equationI(d⁵, d ^N ) = _N + _N cos + _N cos² .Within the accessible range of super-exchange angles 142°156°, the Fe³⁺–O^2––Cr³⁺ interaction is negative (antiferromagnetic). However, a theoretical analysis predicts a sign reversal forI(Fe, Cr.) at about 162° and thus ferromagnetic character of the interaction between 162° and 180°.The spin-only super-exchange interaction integrals fore _g andt _2g electrons, separately, are also calculated. Their angular dependence is accounted for by the behaviour of the antiferromagnetic kinetic and ferromagnetic potential exchange which are of different character when passing from 180° to 90° super-exchange geometry. The magnitude and the sign of the spin-only super-exchange integral for an arbitrary 3d cation, pair is predicted.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

Fuzzy quantum logic II. The logics of unsharp quantum mechanics

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operatorsF on a Hilbert space such that, 0¦F²) the role played by orthomodular posets with respect to orthogonal projections (corresponding to sharp effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (afuzzy-like and anintuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ^* posets, and BZ³ posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.     

Spatial extension of quantum gravitational particles inR 4×K N

It is observed that the magnitude relationma ² l _P/c holds if the non-Euclidean incremental spatial volume associated with a fundamental particle of massm and radiusa is characteristically quantum gravitational in a Kaluza-Klein or superstringR ⁴×K ^N . HereR ⁴ is the four-dimensional Riemannian space-time of general relativity andK ^N is a small-scale, compact,N-dimensional space of characteristic quantum gravitational volumel _P ^N , withl _P (G/c ³)^1/2= 1.61×10^–33 cm denoting the Planck length. For the electron and electron neutrino (assumed to possess nonzero mass bounded empirically by <30 eV) the derived magnitude relationa(l _P/mc)^1/2 yields the estimatesa _e 2.5×10^–22 cm and 3.3×10^–20 cm, spatial extensions which may be detectable by way of fine-scale effects in SSC experiments.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Gravitational (dynamic) time dilation according to absolute space-time theory

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our burst model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal arms, i.e., that at any space point the light velocity (in moving frames the there-and-back velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon.     

Level shift of μ mesoatoms and anomalous interaction of muons with nuclei

The effect of the possible anomalous interaction of a muon with nuclei, due to exchange of the muon and the nucleon, with vector V=⁰, , , J/, , and ⁰ mesons, on the level of the mesoatoms is considered. An estimate is carried out of the energy shift of the 2P-1S transition. A comparison of the estimates obtained for the 2P-1S transition energy shift in the mesoatom²⁰⁶Pb with the experimental data does not contradict the presence in the muon of an anomalous interaction with the nucleon, defined by the effective coupling constant /4 4·10^–4.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 75–80, June, 1978.     

A “hydrodynamic” theory of surface reaction rates

The Brownian motion of adsorbed particles is described in terms of the first four velocity moments of the distribution function (number density, momentum density, energy density and energy current density). The resulting hydrodynamic equations turn out to be sufficient for a simple derivation and extension of Kramers' results for chemical reaction rates in terms of the friction constant of an underlying Fokker-Planck equation. An interpolation formula is obtained for() containing Kramers' results for small and large as limiting cases. For temperaturesT small compared to the well depthV ₀ one finds a large regionT/V ₀/v ₀V ₀/T in which Eyring's absolute rate theory is approximately valid.On leave of absence from Physikdepartment der TUM, München-Garching