S-matrix elements for gauge theories with and without implemented constraints

We derive an expression for the relation between two scattering transition amplitudes which reflect the same dynamics, but which differ in the description of their initial and final state vectors. In one version, the incident and scattered states are elements of a perturbative Fock space, and solve the eigenvalue problem for the `free' part of the Hamiltonian --- the part that remains after the interactions between particle excitations have been `switched off'. Alternatively, the incident and scattered states may be coherent states that are transforms of these Fock states. In earlier work, we reported on the scattering amplitudes for QED, in which a unitary transformation relates perturbative and non-perturbative sets of incident and scattered states. In this work, we generalize this earlier result to the case of transformations that are not necessarily unitary and that may not have unique inverses. We discuss the implication of this relationship for Abelian and non-Abelian gauge theories in which the `transformed', non-perturbative states implement constraints, such as Gauss's law.Comment: 8 pages. Invited contribution to Foundation of Physics for an issue honoring Prof. Lawrence Horwitz on his 65th Birthda

Implementing Gauss's law in Yang-Mills theory and QCD

We construct a transformation that transforms perturbative states into states that implement Gauss's law for `pure gluonic' Yang-Mills theory and QCD. The fact that this transformation is not and cannot be unitary has special significance. Previous work has shown that only states that are unitarily equivalent to perturbative states necessarily give the same S-matrix elements as are obtained with Feynman rules.Comment: 11 page

Gauge-invariant quark and gluon fields in QCD: dynamics, topology, and the Gribov ambiguity

We review the implementation, in a temporal-gauge formulation of QCD, of the non-Abelian Gauss's law and the construction of gauge-invariant gauge and matter fields. We then express the QCD Hamiltonian in terms of these gauge-invariant operator-valued fields, and discuss the relation of this Hamiltonian and the gauge-invariant fields to the corresponding quantities in a Coulomb gauge formulation of QCD. We argue that a representation of QCD in terms of gauge-invariant quantities could be particularly useful for understanding low-energy phenomenology. We present the results of an investigation into the topological properties of the gauge-invariant fields, and show that there are Gribov copies of these gauge-invariant gauge fields, which are constructed in the temporal gauge, even though the conditions that give rise to Gribov copies do not obtain for the gauge-dependent temporal-gauge fields.Comment: 5 pages LaTex; talk presented at light-cone workshop "Particles and Strings", Trento, Italy, September 200

Destroying Hitler’s Berghof: The Bomber Command Raid of 25 April 1945

This paper examines the Royal Air Force raid on Adolf Hitler’s Berghof on the Obersalzberg in April 1945. Arthur Harris, the head of Bomber Command, wanted to emphasize the air power’s decisive role in the defeat of Nazism. However, Winston Churchill and Bernard Montgomery, among others, questioned the usefulness of destroying Berchtesgaden so late in the war. Unlike traditional explanations that focus on post–Dresden guilt, this article contends that British politicians grew increasingly concerned with the economic state of postwar Germany and the potential costs of the upcoming occupation. The continuation of area bombing at this late stage of the war reinforced the fears and consequences of “overkill.” Harris’s disconnect with postwar civil–military concerns negatively influenced the postwar image of Bomber Command

The Defeat of the 12th SS: 7–10 June 1944

In the early hours of 6 June 1944, the first reports of a major Allied operation were transmitted to the 12th SS Hitlerjugend Panzer Division. In anticipation of the long-awaited Allied invasion of occupied France, a company was sent to investigate the Caen area. Though the young soldiers of the division were uncertain of what actually awaited them, the first acts in a conflict that would claim most of their lives were being performed. However, defeat was not on their minds during that hectic morning—the men of the 12th SS were fixed on driving the “little fish” back into the sea