No New Symmetries of the Vacuum Einstein Equations

In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.Comment: 9 pages, Te

Dynamical masses of quarks in quantum chromodynamics

Using Dyson-Schwinger equations we obtain an ultraviolet asymptotics for the dynamical mass of quark in QCD. We also determine a numerical value for the \pi meson decay constant f_\pi.Comment: Electronic version of the published paper, latex, 4 page

Non-perturbative improvement and renormalization of lattice operators

The Alpha Collaboration has proposed an optimal value for c_SW in the Sheikholeslami-Wohlert action, chosen to remove O(a) effects. To measure hadronic matrix elements to the same accuracy we need a method of finding O(a) improved operators, and their renormalization constants. We determine the Z factors by a non-perturbative method, measuring the matrix elements for single quark states propagating through gauge fields in the Landau gauge. The data show large effects coming from chiral symmetry breaking. This allows us to find the improvement coefficients too, by requiring that the amount of chiral symmetry breaking agrees with that predicted by the chiral Ward identities.Comment: 3 pages, Latex, 2 figures, epsf.sty and espcrc2.sty needed. Talk given at Lattice9

Squeezed gluon vacuum and the global colour model of QCD

We discuss how the vacuum model of Celenza and Shakin with a squeezed gluon condensate can explain the existence of an infrared singular gluon propagator frequently used in calculations within the global colour model. In particular, it reproduces a recently proposed QCD-motivated model where low energy chiral parameters were computed as a function of a dynamically generated gluon mass. We show how the strength of the confining interaction of this gluon propagator and the value of the physical gluon condensate may be connected.Comment: 13 pages, LaTe

The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende

Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory

Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory.Comment: 4 pages, no figures; version to be published in Physical Review Letter

Scalars from Top-condensation Models at Hadron Colliders

We study the production and decay of neutral scalars and pseudo-scalars at hadron colliders, in theories where the top-quark mass is the result of a $t\bar t$ condensate. We show that the dominant decay channel for masses below the $t\bar t$ threshold is the flavor changing mode $tc$. This is a consequence of the non-universal nature of the underlying interactions in all top-condensation models and provides a model-independent signature of these scenarios. We show that an upgraded Tevatron is sensitive to a sizeable region of the interesting parameter space and that the LHC will highly constrain these models through this flavor violating channel.Comment: 4 pages, 4 figures. Minor changes in figures for readibility. final version to appear in PR

Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model

We solve the Dyson--Schwinger equation for the quark propagator in a model with singular infrared behavior for the gluon propagator. We require that the solutions, easily found in configuration space, be tempered distributions and thus have Fourier transforms. This severely limits the boundary conditions that the solutions may satisify. The sign of the dimensionful parameter that characterizes the model gluon propagator can be either positive or negative. If the sign is negative, we find a unique solution. It is singular at the origin in momentum space, falls off like $1/p^2$ as $p^2\rightarrow +/-\infty$, and it is truly nonperturbative in that it is singular in the limit that the gluon--quark interaction approaches zero. If the sign of the gluon propagator coefficient is positive, we find solutions that are, in a sense that we exhibit, unconstrained linear combinations of advanced and retarded propagators. These solutions are singular at the origin in momentum space, fall off like $1/p^2$ asympotically, exhibit ``resonant--like" behavior at the position of the bare mass of the quark when the mass is large compared to the dimensionful interaction parameter in the gluon propagator model, and smoothly approach a linear combination of free--quark, advanced and retarded two--point functions in the limit that the interaction approaches zero. In this sense, these solutions behave in an increasingly ``particle--like" manner as the quark becomes heavy. The Feynman propagator and the Wightman function are not tempered distributions and therefore are not acceptable solutions to the Schwinger--Dyson equation in our model. On this basis we advance several arguments to show that the Fourier--transformable solutions we find are consistent with quark confinement, even though they have singularities on th