Genuine twist-3 contributions to the generalized parton distributionsfrom instantons

The genuine twist-3 quark-gluon ( ) contributions to the generalized parton distributions (GPDs) are estimated in the model of the instanton vacuum. These twist-3 effects are found to be parametrically suppressed relative to the kinematical twist-3 ones due to the small packing fraction of the instanton vacuum. We derived exact sum rules for the twist-3 GPDs.Received: 21 April 2004, Published online: 6 August 2004     

A noncommutative deformation of topological field theory

Cohomological Yang–Mills theory is formulated on a noncommutative differentiable four manifold through the -deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the -deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley–Eilenberg homology of noncommutative spacetime and the Chevalley–Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.     

Gauge Fields with Generic Singularities

Let Mbe an n-dimensional manifold equipped with an Abelian Yang–Mills field with connection form . We consider an external potential function Vand examine the existence and regularity of the vortex lines of the form +Vdtwhich define the motion of a particle weakly coupled to the Yang–Mills field on M. These curves are smooth unless the curvature form d is singular and in this paper we treat this singular case from a generic aspect. The problem reduces to the division properties for smooth functions and differential forms, the development of which constitutes the main part of the work presented here.     

Bestimmung der Curietemperatur auf Grund der Anfangssuszeptibilität

Zusammenfassung In der Arbeit wird gezeigt, daß man bei der Curiepunktbestimmung auf Grund der an offenen Proben gemessenen Temperaturabhängigkeit der scheinbaren Aufangssuszeptibilität, bei der üblichen Definition vonT _c mit Hilfe des Wendepunktes dieser Kurve einen systematischen Positivfehler begeht, welcher — sofern uns bekannt ist — außer Beachtung blieb. Dieser Fehler nimmt mit dem Anwachsen des EntmagnetisierungsfaktorsN und des Absolutwertes der wahren Anfangssuszeptibilität ₀ zu und im Gegenteil mit wachsender Abnahmegeschwindigkeit von ₀(T) in der Umgebung vonT _c nimmt er ab. Für kleine Werte des ProduktesN_0max wird im Anhang II eine Näherungsmethode angeführt, nach welcher wir den Curiepunkt mit einem relativ kleinen Fehler bestimmen können.

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In der vorliegenden Arbeit wird gezeigt, daß bei der Bestimmung der Curietemperatur aus dem Wendepunkt des Verlaufes der an offenen Proben gemessenen scheinbaren Anfangssuszeptibilität in Abhängigkeit von der Temperatur ein systematischer positiver Fehler begangen wird. Aus dem Vergleich mit dem experimentell bestimmten Verlaufe der wahren Anfangssuszeptibilität wird die Größe dieses Fehlers für verschiedene EntmagnetisierungsfaktorenN abgeschätz und es werden Näherungsmethoden zu seinem Unterdrücken diskutiert.

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, , , . N , .

     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

Some Properties of the Bel and Bel-Robinson Tensors

The properties of the Bel and Bel-Robinson tensors seem to indicate that they are closely related to the gravitational energy-momentum. We present some new properties of these tensors which might throw some light onto this relationship. First, for any spacetime we find a decomposition of the Bel tensor in terms of the Bel-Robinson tensor and two other tensors, which we call the pure matter super-energy tensor and the matter-gravity coupling super-energy tensor. We show that the pure matter super-energy tensor of any Einstein-Maxwell field is simply the square of the usual energy-momentum tensor. This, together with the fact that the Bel-Robinson tensor has dimensions of energy density square, leads us to the definition of square root for the Bel-Robinson tensor: a two-covariant symmetric traceless tensor with dimensions of energy density and such that its square gives the Bel-Robinson tensor. We prove that this square root exists if and only if the spacetime is of Petrov type O, N or D, and its general expression is explicitly presented. The properties of this new tensor are examined and some interesting explicit examples are analyzed. Of particular interest are an invariant function that appears in the spherically symmetric metrics and an expression for the energy carried out by pure plane gravitational waves. We also examine the decomposition of the whole Bel tensor for Vaidya's radiating metric and Kerr-Newman's solution. Finally, we generalize the definition of square root to a factorization of the Bel-Robinson tensor and get the general solution for all Petrov types.     

The mathematical structure of Newtonian spacetime: Classical dynamics and gravitation

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are timelike vector fields on ) plays a fundamental role in our approach, and the classification of all possible reference frames on is investigated in detail. We succeed in identifying a Lorentzian structure on and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning.     

Creation of Closed or Open Universe from Constrained Instanton

In the no-boundary universe the universe is created from an instanton. However, no instanton exists for the realistic FRW universe with a scalar field. The instanton leading to its quantum creation may be modified and reinterpreted as a constrained gravitational instanton.     

Substantivalism, Relationism, and Structural Spacetime Realism

Debates about the ontological implications of the general theory of relativity have long oscillated between spacetime substantivalism and relationism. I evaluate such debates by claiming that we need a third option, which I refer to as structural spacetime realism. Such a tertium quid sides with the relationists in defending the relational nature of the spacetime structure, but joins the substantivalists in arguing that spacetime exists, at least in part, independently of particular physical objects and events, the degree of independence being given by the extent to which geometrical laws exist over and above physical events exemplifying them. By showing that structural spacetime realism is the natural outcome of a semantic, model-theoretic approach to the nature of scientific theories, I conclude by arguing that the notion of partial isomorphic representation is the most plausible candidate to connect spacetime models with reality.     

Phonon assisted quantum diffusion in a periodic potential

We study the diffusion of a quantum heavy particle moving in a one dimensional strongly corrugated periodic potential, and interacting with a phonon bath.By integrating out the phonons degrees of freedom we derive an effective action functional for the particle, which includes a non-local self-interacting term whose strength is proved to be the classical friction coefficient .Using an instanton approach we express the velocity-velocity correlation function, and thus the mobility, of the brownian particle in terms of the charge density-density correlation function of a classical Coulomb gas, which in the strong corrugation limit has a very low fugacity.By making a virial expansion in the gas fugacity we evaluate the static mobility of the brownian particle as a function of the temperature, and we find two different behaviours: a diffusive behaviour at low friction, where decreases withT, and a localised behaviour at high friction, where increases withT.The cross-over between the two régimes takes place at a critical friction ₀, corresponding to the Kosterlitz-Thouless transition for the Coulomb gas.     

Geometric structures approximated by Maxwell's equations

We show that classical electrodynamics can be obtained as a limit of a system of geodesic equations on 2-vector fields in an Artinian manifold. The limit method is geometrically analogous to the method used to obtain Newtonian mechanics as the limit of the geodesic equations on a Lorentzian manifold. It is also shown that the current and energy-momentum conservation law of electrodynamics can be obtained directly from the geodesic formulation. The geometric structures introduced are related to semi-Kählerian and balanced structures in complex geometry.     

Short and Long SU(2, 2/4) Multiplets in the AdS/CFT Correspondence

We analyze short and long multiplets which appear in the OPE expansion of chiral primary operators in N=4 Super Yang–Mills theory. Among them, higher spin long and new short multiplets appear having the interpretation in the AdS/CFT correspondence of string states and supergravity multiparticle states, respectively. We also analyze the decomposition of long multiplets under N=1 supersymmetry as a possible tool exploring other supersymmetric deformations of IIB string on AdS₅×S₅.     

Quantum probabilities,operators of state preparation,and the principle of superposition

An integrated view concerning the probabilistic organization of quantum mechanics is first obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar space-time structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth probability-trees, complex constructs with treelike space-time support. Though it is strictly entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities: Quantum mechanics appears to be neither a normal probabilistic theory nor an abnormal one, but a pioneering particular realization of afuture extended abstract theory of probabilities. The integrated perception of the probabilistic organization of quantum mechanics removes the current identifications of spectral decompositions of one state vector, with superpositions of several state vectors. This leads to the definition of operators of state preparation and of the calculus with these and to a clear understanding of the physical significance of the principle of superposition. Furthermore, a complement to the quantum theory of measurements is obtained.     

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).     

N=6 Supergravity on Ad S5 and the SU(2,2/3) Superconformal Correspondence

It is argued that N=6 supergravity on Ad S5, with the gauge group SU(3)× U(1) corresponds, at the classical level, to a subsector of the chiral primary operators of N=4 Yang–Mills theories. This projection involves a duality transformation of N=4 Yang–Mills theory and therefore can be valid if the coupling is at a self-dual point, or for those amplitudes that do not depend on the coupling constant.     

On the equivalence of the relativistic theories of gravitation

Einstein's equations are rewritten in terms of a certain torsionless linear connection which differs, in general, from the Levi-Civita metric connection . The torsionless connection appears in a natural way as the canonical momentum of the gravitational field g . Einstein's equations have a simple interpretation in terms of the connection . The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.     

Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach

We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial ⁴. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between localized exotic small R ⁴'s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R ⁴'s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means which may enforce a kind of decoherence.     

The π+ d → pp reaction at intermediate energies

Conclusion The joint efforts of the laboratories with intermediate energies accelerators at ANL, KEK, LANL, LNPI, Saclay, SIN and TRIUMF produced a rather definite picture of the ⁺pp reaction in the isobar region. However the problem of anomalies for the square-root branch point due to the production of isobar in the intermediate state have not been resolved so far. The poles obtained in different phenomenological analyses could be just the effective parametrization of these cuts (see e.g. [13]). Anyway, some singularities are definitely necessary to describe the data.The experimental data in regions s < 2·05 GeV and s < 2·25 GeV are clearly insufficient. Further accumulation of the data in these regions is necessary. Polarized deuteron data are badly needed in the whole kinematical range [13]. Besides as it was mentioned before it is necessary to measure accurately cross sections of other inelastic reactions which are important for the investigation (observation?) of dibaryonsNN N, NN andd N, NN [21]. It would be of interest also to measure cross sections of non quasi two-particle channels likeNN N, 2N andd N, 2N [22]. (In the case ofNN scattering quasi two-particle channels are known to dominate in a wide energy range.)Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.I am grateful to L. A. Kondratyuk, M. G. Ryskin and M. I. Strikman for valuable discussions of the considered problems.     

A plane-symmetric solution of Einstein's equations with perfect fluid and an equation of statep=γϱ

A new class of plane-symmetric solutions of Einstein's equations with perfect fluid source and an equation of statep= (=const.) is presented. It contains the static vacuum solution, a special Kasner solution and the flat Friedmann-Robertson-Walker spacetime as subclasses. The only class for which the matter distribution is truly inhomogeneous (class D in the sequel) represents matter concentrated around a planar orbit of the symmetry group in an expanding universe.     

Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy

We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain TT _c , H0. The analysis is based on numerical data obtained through the Truncated Free Fermion Space Approach. We determine the discontinuities across the Yang–Lee and Langer branch cuts. We confirm the standard analyticity assumptions and propose extended analyticity; roughly speaking, the latter states that the Yang–Lee branching point is the nearest singularity under Langer's branch cut. We support the extended analyticity by evaluating numerically the associated extended dispersion relation.