10,854 research outputs found
Quasi-Local Formulation of Non-Abelian Finite-Element Gauge Theory
Recently it was shown how to formulate the finite-element equations of motion
of a non-Abelian gauge theory, by gauging the free lattice difference
equations, and simultaneously determining the form of the gauge
transformations. In particular, the gauge-covariant field strength was
explicitly constructed, locally, in terms of a path ordered product of
exponentials (link operators). On the other hand, the Dirac and Yang-Mills
equations were nonlocal, involving sums over the entire prior lattice. Earlier,
Matsuyama had proposed a local Dirac equation constructed from just the
above-mentioned link operators. Here, we show how his scheme, which is closely
related to our earlier one, can be implemented for a non-Abelian gauge theory.
Although both Dirac and Yang-Mills equations are now local, the field strength
is not. The technique is illustrated with a direct calculation of the current
anomalies in two and four space-time dimensions. Unfortunately, unlike the
original finite-element proposal, this scheme is in general nonunitary.Comment: 19 pages, REVTeX, no figure
Casimir Energies and Pressures for -function Potentials
The Casimir energies and pressures for a massless scalar field associated
with -function potentials in 1+1 and 3+1 dimensions are calculated. For
parallel plane surfaces, the results are finite, coincide with the pressures
associated with Dirichlet planes in the limit of strong coupling, and for weak
coupling do not possess a power-series expansion in 1+1 dimension. The relation
between Casimir energies and Casimir pressures is clarified,and the former are
shown to involve surface terms. The Casimir energy for a -function
spherical shell in 3+1 dimensions has an expression that reduces to the
familiar result for a Dirichlet shell in the strong-coupling limit. However,
the Casimir energy for finite coupling possesses a logarithmic divergence first
appearing in third order in the weak-coupling expansion, which seems
unremovable. The corresponding energies and pressures for a derivative of a
-function potential for the same spherical geometry generalizes the TM
contributions of electrodynamics. Cancellation of divergences can occur between
the TE (-function) and TM (derivative of -function) Casimir
energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX
A novel scene-recording spectroradiometer
In this paper we describe an innovative approach to providing both a
synthesised dual-beam capability and a permanent photographic record of the
precise area sensed by a spectroradiometer. These advances have been achieved
without modifying the spectroradiometer and may be used with a wide range of
commercially-available spectroradiometers
Continued Fraction as a Discrete Nonlinear Transform
The connection between a Taylor series and a continued-fraction involves a
nonlinear relation between the Taylor coefficients and the
continued-fraction coefficients . In many instances it turns out
that this nonlinear relation transforms a complicated sequence into
a very simple one . We illustrate this simplification in the context
of graph combinatorics.Comment: 6 pages, OKHEP-93-0
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases
We review the theoretical bounds on the effective properties of linear
elastic inhomogeneous solids (including composite materials) in the presence of
constituents having non-positive-definite elastic moduli (so-called
negative-stiffness phases). We show that for statically stable bodies the
classical displacement-based variational principles for Dirichlet and Neumann
boundary problems hold but that the dual variational principle for traction
boundary problems does not apply. We illustrate our findings by the example of
a coated spherical inclusion whose stability conditions are obtained from the
variational principles. We further show that the classical Voigt upper bound on
the linear elastic moduli in multi-phase inhomogeneous bodies and composites
applies and that it imposes a stability condition: overall stability requires
that the effective moduli do not surpass the Voigt upper bound. This
particularly implies that, while the geometric constraints among constituents
in a composite can stabilize negative-stiffness phases, the stabilization is
insufficient to allow for extreme overall static elastic moduli (exceeding
those of the constituents). Stronger bounds on the effective elastic moduli of
isotropic composites can be obtained from the Hashin-Shtrikman variational
inequalities, which are also shown to hold in the presence of negative
stiffness
The 'psychic pet' phenomenon: a reply to Rupert Sheldrake
Original article can be found at: http://www.spr.ac.uk/expcms/Rupert Sheldrake (1999a) has published a note in the previous issue of the Journal criticising our research into the âpsychic petâ phenomenon. Certain points arising from this criticism have also been included in his recent book, Dogs That Know When Their Owners Are Coming Home and Other Unexplained Powers of Animals (Sheldrake 1999b). This paper outlines why we believe his criticisms to be invalid.Peer reviewe
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