Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.Comment: 14 pages, 9 figures. v2: Typos corrected. v3: added a new section discussing alternative (new variables) approaches, and fixed a problem with the appearance of figures in the pdf version. Version to appear in Phys Rev

Continuum Singularities of a Mean Field Theory of Collisions

Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $\chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater determinant $\phi$ of single particle states $\phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|\phi_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {\it inhomogeneous} TIMF equations are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure

Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism

Perturbative Coulomb gauge Yang-Mills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the two-point functions at one-loop order are derived. It is shown how the non-ultraviolet divergent parts of the results are finite at spacelike momenta with kinematical singularities on the light-cone and subsequent branch cuts extending into the timelike region.Comment: 23 pages, 6 figure

Analysis of reinforced concrete structures with occurrence of discrete cracks at arbitrary positions

A nonlinear analysis of in-plane loaded plates is presented, which eliminates the disadvantages of the smeared crack approach. The elements used and the computational method are discussed. An example is shown in which one or more discrete cracks are dominant

The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.Comment: 10 LaTeX pages 4 figures, report no UNITU-THEP-7/199

Self-Consistent Pushing and Cranking Corrections to the Meson Fields of the Chiral Quark-Loop Soliton

We study translational and spin-isospin symmetry restoration for the two-flavor chiral quark-loop soliton. Instead of a static soliton at rest we consider a boosted and rotating hedgehog soliton. Corrected classical meson fields are obtained by minimizing a corrected energy functional which has been derived by semi-classical methods ('variation after projection'). We evaluate corrected meson fields in the region 300 MeV \le M \le 600 MeV of constituent quark masses M and compare them with the uncorrected fields. We study the effect of the corrections on various expectation values of nuclear observables such as the root-mean square radius, the axial-vector coupling constant, magnetic moments and the delta-nucleon mass splitting.Comment: 19 pages, LaTeX, 7 postscript figures included using 'psfig.sty', to appear in Int.J.Mod.Phys.

Color Screening, Casimir Scaling, and Domain Structure in G(2) and SU(N) Gauge Theories

We argue that screening of higher-representation color charges by gluons implies a domain structure in the vacuum state of non-abelian gauge theories, with the color magnetic flux in each domain quantized in units corresponding to the gauge group center. Casimir scaling of string tensions at intermediate distances results from random spatial variations in the color magnetic flux within each domain. The exceptional G(2) gauge group is an example rather than an exception to this picture, although for G(2) there is only one type of vacuum domain, corresponding to the single element of the gauge group center. We present some numerical results for G(2) intermediate string tensions and Polyakov lines, as well as results for certain gauge-dependent projected quantities. In this context, we discuss critically the idea of projecting link variables to a subgroup of the gauge group. It is argued that such projections are useful only when the representation-dependence of the string tension, at some distance scale, is given by the representation of the subgroup.Comment: 24 pages, 14 figures; v2: references added; v3: published version containing some additional introductory discussio

On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.Comment: 24 pages, 4 eps-figures; new version matches published on