35,847 research outputs found
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 Hitlerâs Berghof: The Bomber Command Raid of 25 April 1945
This paper examines the Royal Air Force raid on Adolf Hitlerâs Berghof on the Obersalzberg in April 1945. Arthur Harris, the head of Bomber Command, wanted to emphasize the air powerâs 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 postâDresden 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 âoverkill.â Harrisâs disconnect with postwar civilâmilitary concerns negatively influenced the postwar image of Bomber Command
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