William H. Klink

Covariant nucleon electromagnetic form factors from the Goldstone-boson-exchange quark model

Abstract We present a study of proton and neutron electromagnetic form factors for the recently proposed Goldstone-boson-exchange constituent quark model. Results for charge radii, magnetic moments, and electric as well as magnetic form factors are reported. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. All the predictions by the Goldstone-boson-exchange constituent quark model are found to fall remarkably close to existing experimental data.

Covariant axial form factor of the nucleon in a chiral constituent quark model

Abstract The axial form factor G A of the nucleon is investigated for the Goldstone-boson-exchange constituent quark model using the point-form approach to relativistic quantum mechanics. The results, being covariant, show large contributions from relativistic boost effects. The predictions are obtained directly from the quark-model wave functions, without any further input such as vertex or constituent-quark form factors, and fall remarkably close to the available experimental data.

Constructing point form mass operators from vertex interactions

Abstract A relativistic few-body theory is formulated using point form quantum mechanics, in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. The four-momentum operator is written as a product of mass and four-velocity operators, where the mass operator is the sum of free and interacting mass operators. Interacting mass operators are constructed from vertices, products of local field operators, evaluated at the space–time point zero. Matrix elements of such mass operators, evaluated on four-velocity eigenstates of a truncated Fock space, which is the space of the few-body theory, are shown to behave like relativistic potentials. Examples for a simple vertex are given.

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincaré invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark–antiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space–time hyperboloid could be advantageous.

Constructing and Testing Theological Models

In order for theology to have a cognitive dimension, it is necessary to have procedures for testing and critically evaluating theological models. We make use of certain features of scientific models to show how science has been able to move beyond the poles of foundationalisin, represented by logical positivism, and antifoundationalism or relativism, represented by the sociologists of knowledge. These ideas are generalized to show that constructing and testing theological models similarly offers a means by which theology can move beyond confessionalism and postmodernism. Our starting point is Paul Tillichs concept of God as the ground of being and the different levels of consciousness and thinking that accompany his understanding of theology. The ontological argument of Anselm is shown to play a key role, not as a proof for the existence of God but as a means for testing theological models. An example of a theological model, drawn from the domain of philosophy of science, is presented to show how theological models are constructed and tested.

Electromagnetic meson form factor from a relativistic coupled-channels approach

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for spacelike momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the qqe and qqe{gamma} states. With the approximation that the total velocity of the qqe system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the qqe{gamma} channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the q{sup +}=0 reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.

n-Fold tensor products of GL(N, C) and decomposition of Fock spaces

Abstract Fock spaces over n × N complex matrices are introduced to deal with the reduction of n-fold tensor products of representations of GL(N, C ). These spaces are decomposed into orthogonal direct sums of finite-dimensional polynomial spaces P (M) that are invariant under GL(N, C ). A Frobenius reciprocity theorem is proved which relates the number of times an irreducible representation of GL(N, C ) appears in P (M) to the number of times this irreducible representation contains a representation of its diagonal subgroup. A GL(n, C ) action is shown to commute with the GL(N, C ) action and is used to find maps that send irreducible representations of GL(N, C ) into the P (M) spaces. Invariant Casimir operators are introduced to deal with the multiplicity occurring in n-fold tensor products.

Calculation of Clebsch-Gordan and Racah coefficients using symbolic manipulatio n programs

A procedure for calculating Clebsch--Gordan and Racah coefficients arising from the decomposition of n-fold tensor products of the U(N) groups using symbolic manipulation programs is given. Basic states are realized as polynomials in a space equipped with a differentiation inner product. The desired coefficients are then obtained by differentiating the relevant polynomials. Examples from SU(2) and SU(3) are given. copyright 1989 Academic Press, Inc.

On the reduction of n-fold tensor product representations of noncompact groups

The reduction ofn-fold tensor products of induced unitary representations of noncompact groups into irreducible constituents is shown. Clebsch-Gordon coefficients are then calculated. The technique is applied to then-fold tensor products of the positive mass representations of the Poincaré group.

Vector mesons in a relativistic point-form approach

We apply the point form of relativistic quantum mechanics to develop a Poincare invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange. This approach takes the exchange particle explicitly into account and leads to a generalized eigenvalue equation for the Bakamjian-Thomas type mass operator of the system. The coupling of the exchange particle is derived from quantum field theory. As an illustrative example we consider vector mesons within the chiral constituent quark model in which the hyperfine interaction between the confined quark-antiquark pair is generated by Goldstone-boson exchange. We study the effect of retardation in the Goldstone-boson exchange by comparing with the commonly used instantaneous approximation. As a nice physical feature we find that the problem of a too large