16,319 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
Influence of Water Depth on the Rate of Expansion of Giant Cutgrass Populations and Management Implications
Giant cutgrass (
Zizaniopsis miliacea
(Michx.) Doell. &
Asch.), a tall emergent grass native to the southeastern United
States, was studied in Lake Seminole where it formed
large expanding stands, and Lake Alice where it was confined
to a stable narrow fringe
Quantum Gauge Equivalence in QED
We discuss gauge transformations in QED coupled to a charged spinor field,
and examine whether we can gauge-transform the entire formulation of the theory
from one gauge to another, so that not only the gauge and spinor fields, but
also the forms of the operator-valued Hamiltonians are transformed. The
discussion includes the covariant gauge, in which the gauge condition and
Gauss's law are not primary constraints on operator-valued quantities; it also
includes the Coulomb gauge, and the spatial axial gauge, in which the
constraints are imposed on operator-valued fields by applying the
Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and
spatial axial gauges to what we call
``common form,'' in which all particle excitation modes have identical
properties. We also show that, once that common form has been reached, QED in
different gauges has a common time-evolution operator that defines
time-translation for states that represent systems of electrons and photons.
By combining gauge transformations with changes of representation from
standard to common form, the entire apparatus of a gauge theory can be
transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring
Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn
van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages,
REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author
Computing in unipotent and reductive algebraic groups
The unipotent groups are an important class of algebraic groups. We show that
techniques used to compute with finitely generated nilpotent groups carry over
to unipotent groups. We concentrate particularly on the maximal unipotent
subgroup of a split reductive group and show how this improves computation in
the reductive group itself.Comment: 22 page
Gauge equivalence in QCD: the Weyl and Coulomb gauges
The Weyl-gauge ( QCD Hamiltonian is unitarily transformed to a
representation in which it is expressed entirely in terms of gauge-invariant
quark and gluon fields. In a subspace of gauge-invariant states we have
constructed that implement the non-Abelian Gauss's law, this unitarily
transformed Weyl-gauge Hamiltonian can be further transformed and, under
appropriate circumstances, can be identified with the QCD Hamiltonian in the
Coulomb gauge. We demonstrate an isomorphism that materially facilitates the
application of this Hamiltonian to a variety of physical processes, including
the evaluation of -matrix elements. This isomorphism relates the
gauge-invariant representation of the Hamiltonian and the required set of
gauge-invariant states to a Hamiltonian of the same functional form but
dependent on ordinary unconstrained Weyl-gauge fields operating within a space
of ``standard'' perturbative states. The fact that the gauge-invariant
chromoelectric field is not hermitian has important implications for the
functional form of the Hamiltonian finally obtained. When this nonhermiticity
is taken into account, the ``extra'' vertices in Christ and Lee's Coulomb-gauge
Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity
is neglected, the Hamiltonian used in the earlier work of Gribov and others
results.Comment: 25 page
Analysis and design of a flat central finned-tube radiator
Computer program based on fixed conductance parameter yields minimum weight design. Second program employs variable conductance parameter and variable ratio of fin length to tube outside radius, and is used for radiator designs with geometric limitations. Major outputs of the two programs are given
Performance and materials aspects of Ge:Be photoconductors
Ge:Be photoconductors were developed for low photon background applications in the 30 to 50 MM wavelength region. These detectors provide higher responsivity and lower noise equivalent power (NEP) than the Ge:Ga detectors currently operating in this wavelength range. Beryllium doped single crystals were grown by the Czochralski method from a carbon susceptor under a vacuum of approx. one million torr. An optimum detective quantum efficiency of 46% at a background flux of 1.5 x 10 to the 8th power photons/second (7 x 10 to the 13th power W) was reported. Ge:Be detector performance is strongly influenced by the absolute concentrations and the concentration ratio of residual shallow donors and shallow acceptors
Topology of the gauge-invariant gauge field in two-color QCD
We investigate solutions to a nonlinear integral equation which has a central
role in implementing the non-Abelian Gauss's Law and in constructing
gauge-invariant quark and gluon fields. Here we concern ourselves with
solutions to this same equation that are not operator-valued, but are functions
of spatial variables and carry spatial and SU(2) indices. We obtain an
expression for the gauge-invariant gauge field in two-color QCD, define an
index that we will refer to as the ``winding number'' that characterizes it,
and show that this winding number is invariant to a small gauge transformation
of the gauge field on which our construction of the gauge-invariant gauge field
is based. We discuss the role of this gauge field in determining the winding
number of the gauge-invariant gauge field. We also show that when the winding
number of the gauge field is an integer , the gauge-invariant
gauge field manifests winding numbers that are not integers, and are
half-integers only when .Comment: 26 pages including 6 encapsulated postscript figures. Numerical
errors have been correcte
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