Nucleon pair structure of realistic many body wave functions

The scalar part of the two-body density is calculated for the²⁰Ne ground band and for the yrast 2⁺ state in⁶⁸Ge as obtained by solving the Hartree-Fock-Bogoliubov problem with symmetry-projection before the variation. The nucleon pair structure of these states is analysed and the results obtained with different effective Hamiltonians are compared.Work supported by the IPNE, Bucharest, Romania under Contract No. 60-92-7, the DFG and the Internationales Büro des KfK Karlsruhe, Germany     

Sum rules for baryonic vertex functions and the proton wave function in QCD

We consider light-cone sum rules for vertex functions involving baryon-meson couplings. These sum rules relate the non-pertubative, and experimentally known, coupling constants to the moments of the wave function of the proton state. Our results for these moments are consistent with those obtained from QCD sum rules for two-point functions.     

Nucleon structure functions from high energy neutrino interactions

Structure functions obtained from high energy neutrino and antineutrino scattering from an iron target are presented. These were extracted from the combined data of Fermilab experiments E616 and E701; these utilized narrow band beam runs between 1979–1982. The structure functions are used to test the validity of quarkparton model (QPM) predictions and to extract the QCD scale parameter Λ from fits to the Altarelli-Parisi equations.     

Local renormalizable gauge theories from nonlocal operators

The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

Nucleon electroweak form factors: Analysis of their spectral functions

We investigate the imaginary parts of the nucleon electromagnetic and axial form factors close to threshold in the framework of heavy baryon chiral perturbation theory. For the isovector electromagnetic form factors, we recover the well-known strong enhancement near threshold. For the isoscalar ones, we show that there is no visible enhancement due to the three-pion continuum. This justifies the use of vector meson poles only in dispersion-theoretical calculations. We also calculate the imaginary part of the nucleon isovector axial form factor and show that it is small in the threshold region.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

Renormalization of composite operators in gauge theories

We give a logically complete treatment of the renormalization of composite operators in gauge theories.     

Renormalization of Wilson operators in gauge theories

The operators in a Wilson expansion are not in general multiplicatively renormalized in non-Abelian gauge theories. This is because of the renormalization of the gauge transformations themselves. Renormalized fields may be defined, which have the old gauge transformations. Alternatively, a special choice of gauge may be made, in which the gauge transformations are unchanged on renormalization. In any case, one gauge invariant factor appears in the renormalization of the Wilson operators.     

Origin of logarithmic operators in conformal field theories

We study logarithmic operators in Coulomb gas models, and show that they occur when the “puncture” operator of the Liouville theory is included in the model. We also consider WZNW models for SL(2,R), and for SU(2) at level 0, in which we find logarithmic operators which form Jordan blocks for the current as well as the Virasoro algebra.     

Green functions of vortex operators

We study the euclidean Green functions of the 't Hooft vortex operator, primarily for abelian gauge theories. The operator is written in terms of elementary fields, with emphasis on a form in which it appears as the exponential of a surface integral. We explore the requirement that the Green functions depend only on the boundary of this surface. The Dirac veto problem appears in a new guise. We present a two-dimensional “solvable model” of a Dirac string, which suggests a new solution of the veto problem. The renormalization of the Green functions of the abelian Wilson loop and abelian vortex operator is studied with the aid of the operator product expansion. In each case, an overall multiplication of the operator makes all Green functions finite; a surprising cancellation of divergences occurs with the vortex operator. We present a brief discussion of the relation between the nature of the vacuum and the cluster properties of the Green functions of the Wilson and vortex operators, for a general gauge theory. The surface-like cluster property of the vortex operator in an abelian Higgs theory is explored in more detail.     

Determination of heavy-meson wave functions from B decays

We extract the B, D, and meson wave functions from the CLEO data of the decays and in the perturbative QCD framework. In this formalism, various logarithmic corrections are organized to give the Wilson evolution from the W boson mass down to the characteristic scale of a decay process, which is of order of the b quark mass, and the Sudakov evolution from the characteristic scale to a lower factorization scale of order . With large logarithms organized, the b quark decay amplitudes are evaluated reliably in perturbation theory. Below the factorization scale, QCD dynamics is regarded as being nonperturbative, and absorbed into meson wave functions. Because of their universality, the heavy-meson wave functions determined in this work, can be employed to make predictions of other decay modes. We also observe that the dependence of heavy meson wave functions on intrinsic parton transverse momenta plays an important role in the explanation of data. Received: 18 February 1999 / Revised version: 24 June 1999 / Published online: 3 November 1999     

Bernstein operators and super-Schur functions: combinatorial aspects

Letters in Mathematical Physics - The Bernstein vertex operators, which can be used to build recursively the Schur functions, are extended to superspace. Four families of super vertex operators are...     

Lithium crystal properties from high-quality Hartree-Fock wave functions

Properties derived from lithium b.c.c. crystal Hartree-Fock (HF) calculations, using LCAO-type Bloch functions and including 2s, 2p and 3d Slater-type basis orbitals, are presented. These include total energies, lattice parameters, band gaps, widths of the occupied part of valence band, bulk modulus and Fermi surface geometry. Energetic quantities are in qualitative agreement with our earlier work. Their disagreements with experiment again underscore some inadequacies of HF. The bulk modulus is overestimated by about 50%, which is typical for HF-based molecular force constants. The Fermi surface is calculated to have a maximum distortion (in the 〈110〉 direction) of about 3.5%. This is in agreement with the best experiments. The sensitivity of predicted distortions to Brillouin zone integration points is discussed.