Assessing Responsibility: Fixing Blame versus Fixing Problems

In the midst of even the most tragic circumstances attending the aftermath of disaster, and co-existing with a host of complex emotions, arises a practical consideration: how might similar tragedies be prevented in the future? The complexity of such situations must not be neglected. More than mere prevention must usually be taken into consideration. But the practical question is of considerable importance. In what follows, I will offer some reasons for being concerned that efforts to fix the problem -- efforts, that is, directed toward insuring that similar tragedies do not occur in the future -- can easily be obstructed by attempts to fix blame -- that is, efforts directed toward determining which agent among those involved is guilty of wrong-doing. This is the case, I shall contend, even where some agent or another really is guilty of wrong-doing. The problem is further complicated by a pervasive human tendency to imagine that some agent or another must be responsible in some way for any tragedy that occurs -- even when this is not really true -- but its influence is not at all limited to such cases. As I shall suggest, philosophical attitudes toward issues of determinism and free will may be implicated in the different approaches people take to the problem of assessing what has gone wrong in a particular case and how to fix it, but such deep philosophical problems need not be resolved here. The point is not that humans are never guilty of wrong-doing (since their actions, the argument might go, are all products of outside forces), but rather that whatever the case may be about guilt, tracking down guilty persons is a different business from fixing institutionally-embedded problems so as to lessen the likelihood of their recurrence

The new definition of lattice gauge fields and the Landau gauge

The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing algorithm is presented. Performance of the smeared gauge fixing in SU(3) is also investigated.Comment: LATTICE98(Algorithms) 3 pages 3, 3 eps figure

Gauge fixing in (2+1)-gravity with vanishing cosmological constant

We apply Dirac's gauge fixing procedure to (2+1)-gravity with vanishing cosmological constant. For general gauge fixing conditions based on two point particles, this yields explicit expressions for the Dirac bracket. We explain how gauge fixing is related to the introduction of an observer into the theory and show that the Dirac bracket is determined by a classical dynamical r-matrix. Its two dynamical variables correspond to the mass and spin of a cone that describes the residual degrees of freedom of the spacetime. We show that different gauge fixing conditions and different choices of observers are related by dynamical Poincar\'e transformations. This allows us to locally classify all Dirac brackets resulting from the gauge fixing and to relate them to a set of particularly simple solutions associated with the centre-of-mass frame of the spacetime.Comment: Talk given at the Workshop on Noncommutative Field Theory and Gravity Corfu, September 7 - 11, 2011; 20 pages, 6 figure

Topological gauge fixing

We implement the metric-independent Fock-Schwinger gauge in the abelian quantum Chern-Simons field theory defined in ${\mathbb R}^3$. The expressions of the various components of the propagator are determined. Although the gauge field propagator differs from the Gauss linking density, we prove that its integral along two oriented knots is equal to the linking number

Fixing Einstein's equations

Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in special coordinates). That is, they do not produce unique solutions that depend smoothly on the initial data. To remedy this failing, there has been widespread interest recently in reformulating Einstein's theory as a hyperbolic system of differential equations. The physical and geometrical content of the original theory remain unchanged, but dynamical evolution is made sound. Here we present a new hyperbolic formulation in terms of $g_{ij}$, $K_{ij}$, and \bGam_{kij} that is strikingly close to the space-plus-time (``3+1'') form of Einstein's original equations. Indeed, the familiarity of its constituents make the existence of this formulation all the more unexpected. This is the most economical first-order symmetrizable hyperbolic formulation presently known to us that has only physical characteristic speeds, either zero or the speed of light, for all (non-matter) variables. This system clarifies the relationships between Einstein's original equations and the Einstein-Ricci and Frittelli-Reula hyperbolic formulations of general relativity and establishes links to other hyperbolic formulations.Comment: 8 pages, revte

Preconditioning Maximal Center Gauge with Stout Link Smearing in SU(3)

Center vortices are studied in SU(3) gauge theory using Maximal Center Gauge (MCG) fixing. Stout link smearing and over-improved stout link smearing are used to construct a preconditioning gauge field transformation, applied to the original gauge field before fixing to MCG. We find that preconditioning successfully achieves higher gauge fixing maxima. We observe a reduction in the number of identified vortices when preconditioning is used, and also a reduction in the vortex-only string tension.Comment: 9 pages, 4 figure

Background field method in the gradient flow

In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom. In the present paper, we consider a modified form of the gauge-fixing term that manifestly preserves covariance under the background gauge transformation. It is shown that our gauge-fixing term does not affect gauge-invariant quantities as the conventional gauge-fixing term. The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion. The formulation can be generalized to systems containing fermions.Comment: 19 pages, the final version to appear in PTE