Discrete phase space II. Relativistic lattice wave equations and divergence-free green's functions

Therelativistic lattice Klein-Gordon equation, Dirac equation, electromagnetic equations, and gauge field equations are presented as partialdifference equations. Various lattice Green's functions are constructed (except for non-abelian gauge fields). It is proved that many of the lattice Green's functions are non-singular or divergence-free. Moreover, it is conjectured that all lattice Green's functions are non-singular.     

Regularity and decay of lattice Green's functions

In the paper we study a class of lattice, covariant Laplace operators with external gauge fields. We prove that these operators are positive and that their Green's functions decay exponentially. They also have regularity properties similar to continuous space Green's functions. All the bounds are uniform in the lattice spacing.     

Euclidean Green's functions for Jaffe fields

We extend the axioms for Euclidean Green's functions recently proposed by Osterwalder and Schrader to Jaffe fields.     

On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive , , and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections. Received: 12 November 1997 / Published online: 26 February 1998     

Relativistic theory of fermions and classical fields on a collocation lattice

We present a novel numerical method for solving dynamical strong field problems in quantum mechanics and classical field theory based on expansion of functions in terms of splines. The method differs from traditional approaches by the introduction of a mapping onto a collocation lattice, which is generally nonuniform and time dependent depending on the particular physical application. This approach results in a set of finite matrix transformations of a type which can be evaluated rapidly on supercomputers possessing either vector or matrix coprocessors. As an example of the method, we present a study of the relativistic quantum-mechanical many-electron problem interacting via very strong time-dependent classical fields.     

Structure functions and parton distributions

We review recent developments in the determination of parton densities from deep inelastic and related data. We show how the asymmetries observed in theW ^± rapidity distributions and inpp/pn Drell-Yan production further constrain the partons at moderatex.     

Green's functions on finite lattices and their connection to the infinite lattice limit

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of a translation operator. Explicit examples are given for one- and two-dimensional lattices.     

Jets and quark confinement in the covariant parton model

A parton model incorporating quark confinement is discussed which (a) reproduces conventional parton model cross sections for deep inelastic lepton scattering and for large-p_T hadronic phenomena, (b) leads to final state jets and (c) accounts for the similar multiplicities observed in hadronic and lepton induced final states at low p_T.     

Structure functions and parton distributions

We review recent developments in the determination of parton densities from deep inelastic and related data. We show how the asymmetries observed in theW ^± rapidity distributions and inpp/pn Drell-Yan production further constrain the partons at moderatex.     

Relativistic harmonic confinement of quarks and gluons

A current confinement model for glue-balls is proposed to maintain complete similarity with relativistic harmonic oscillator model (rhm) with Lorentz scalar and vector potentials for quarks. The spurious motion of the centre of confinement is accounted for in these models in exactly the same manner. We shall review some of the successes of therhm in hardronic masses, magnetic moments of baryons, nucleonic sizes and polarisability and proton-antiproton annihilation, as well as the recent results on glue-balls.     

Spin-dependent parton distributions and structure functions

Nuclear parton distributions and structure functions are determined in an effective chiral quark theory. We also discuss an extension of our model to fragmentation functions.     

Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence-free vector field in R³ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial with the same degree.     

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α_s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.     

Relativistic Hamiltonian dynamics. II. Momentum-dependent interactions, confinement and quantization

The previously developed covariant classical relativistic N-particle dynamics is extended to momentum-dependent interactions and generalized to a gauge-independent constraint reduction. This reduction is made via center-of-momentum variables as well as via the more conventional individual particle variables. A canonical quantization is then carried out. The two-body problem is discussed in detail for the case of momentum-dependent interactions. It is demonstrated that such interactions can give rise to dynamical confinement both classically and quantum mechanically. The prototype interaction −β²(ξ · π)² has a harmonic oscillator type spectrum and shows a linear dependence of the binding energy on the angular momentum for small particle rest masses (m₁, m₂ β).     

Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.