5,238 research outputs found
Conformal Field Theories, Representations and Lattice Constructions
An account is given of the structure and representations of chiral bosonic
meromorphic conformal field theories (CFT's), and, in particular, the
conditions under which such a CFT may be extended by a representation to form a
new theory. This general approach is illustrated by considering the untwisted
and -twisted theories, and respectively,
which may be constructed from a suitable even Euclidean lattice .
Similarly, one may construct lattices and by
analogous constructions from a doubly-even binary code . In the case when
is self-dual, the corresponding lattices are also. Similarly,
and are self-dual if and only if is. We show that
has a natural ``triality'' structure, which induces an
isomorphism and also a triality
structure on . For the Golay code,
is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an
extension of) Conway's group on this theory to the Monster, so setting triality
and Frenkel, Lepowsky and Meurman's construction of the natural Monster module
in a more general context. The results also serve to shed some light on the
classification of self-dual CFT's. We find that of the 48 theories
and with central charge 24 that there are 39 distinct ones,
and further that all 9 coincidences are accounted for by the isomorphism
detailed above, induced by the existence of a doubly-even self-dual binary
code.Comment: 65 page
Electromagnetic field application to underground power cable detection
Before commencing excavation or other work where power or other cables may be buried, it is important to determine the location of cables to ensure that they are not damaged. This paper describes a method of power-cable detection and location that uses measurements of the magnetic field produced by the currents in the cable, and presents the results of tests performed to evaluate the method. The cable detection and location program works by comparing the measured magnetic field signal with values predicted using a simple numerical model of the cable. Search coils are used as magnetic field sensors, and a measurement system is setup to measure the magnetic field of an underground power cable at a number of points above the ground so that it can detect the presence of an underground power cable and estimate its position. Experimental investigations were carried out using a model and under real site test conditions. The results show that the measurement system and cable location method give a reasonable prediction for the position of the target cable
Detection and Location of Underground Power Cable using Magnetic Field Technologies
The location of buried underground electricity cables is becoming a major engineering and social issue worldwide. Records of utility locations are relatively scant, and even when records are available, they almost always refer to positions relative to ground-level physical features that may no longer exist or that may have been moved or altered. The lack of accurate positioning records of existing services can cause engineering and construction delays and safety hazards when new construction, repairs, or upgrades are necessary. Hitting unknown underground obstructions has the potential to cause property damage, injuries and, even deaths. Thus, before commencing excavation or other work where power or other cables may be buried, it is important to determine the location of the cables to ensure that they are not damaged during the work. This paper describes the use of an array of passive magnetic sensors (induction coils) together with signal processing techniques to detect and locate underground power cables. The array consists of seven identical coils mounted on a support frame; one of these coils was previously tested under laboratory conditions, and relevant results have been published in [1]. A measurement system was constructed that uses a battery powered data acquisition system with two NI 9239 modules connected to the coil array, and controlled by a laptop. The system is designed to measure the magnetic field of an underground power cable at a number of points above the ground. A 3 by 3 m test area was chosen in one of our campus car parks. This area was chosen because the university’s utility map shows an isolated power cable there. Measurements were taken with the array in 16 different test positions, and compared with the values predicted for a long straight horizontal cable at various positions. Finally, error maps were plotted for different Z-coordinate values, showing the minimum fitting error for each position in this plane. One such map is shown in Figure 1; the low error values of 4-5% give a high degree of confidence that most of the measured signal is due to a cable near to these positions. This view is supported by the fact that the university’s utility map shows the cable at X = 1.4 m, and by amplitude measurements taken with a hand-held magnetic field meter
Explicit Construction of Spin 4 Casimir Operator in the Coset Model
We generalize the Goddard-Kent-Olive (GKO) coset construction to the
dimension 5/2 operator for and compute the fourth order
Casimir invariant in the coset model with the generic unitary minimal
series that can be viewed as perturbations of the
limit, which has been investigated previously in the realization of
free fermion model.Comment: 11 page
On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine
We consider the relationship between the conjectured uniqueness of the
Moonshine Module, , and Monstrous Moonshine, the genus zero
property of the modular invariance group for each Monster group Thompson
series. We first discuss a family of possible meromorphic orbifold
constructions of based on automorphisms of the Leech
lattice compactified bosonic string. We reproduce the Thompson series for all
51 non-Fricke classes of the Monster group together with a new relationship
between the centralisers of these classes and 51 corresponding Conway group
centralisers (generalising a well-known relationship for 5 such classes).
Assuming that is unique, we then consider meromorphic
orbifoldings of and show that Monstrous Moonshine holds if
and only if the only meromorphic orbifoldings of give
itself or the Leech theory. This constraint on the
meromorphic orbifoldings of therefore relates Monstrous
Moonshine to the uniqueness of in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0
Signature Characters for A_2 and B_2
The signatures of the inner product matrices on a Lie algebra's highest
weight representation are encoded in the representation's signature character.
We show that the signature characters of a finite-dimensional Lie algebra's
highest weight representations obey simple difference equations that have a
unique solution once appropriate boundary conditions are imposed. We use these
results to derive the signature characters of all and highest
weight representations. Our results extend, and explain, signature patterns
analogous to those observed by Friedan, Qiu and Shenker in the Virasoro
algebra's representation theory.Comment: 22 p
Interacting Electrons and Localized Spins: Exact Results from Conformal Field Theory
We give a brief review of the Kondo effect in a one-dimensional interacting
electron system, and present exact results for the impurity thermodynamic
response based on conformal field theory.Comment: 6 pages LaTeX. To appear in the Proceedings of the 1995 Schladming
Winter School on Low-Dimensional Models in Statistical Physics and Quantum
Field Theor
Folding the W Algebras
In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1})
produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda
model based on B_n (resp. C_n) can be seen as resulting from the folding of a
W-algebra based on A_{2n} (resp. A_{2n-1}). More generally, W algebras related
to the B-C-D algebra series can appear from W algebras related to the unitary
ones. Such an approach is in particular well adapted to obtain fusion rules of
W algebras based on non simply laced algebras from fusion rules corresponding
to the A_n case. Anagously, super W algebras associated to orthosymplectic
superalgebras are deduced from those relative to the unitary A(m,n) series.Comment: 27 pages, Late
On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
We clarify the notion of the DS --- generalized Drinfeld-Sokolov ---
reduction approach to classical -algebras. We first strengthen an
earlier theorem which showed that an embedding can be associated to every DS reduction. We then use the fact that a
\W-algebra must have a quasi-primary basis to derive severe restrictions on
the possible reductions corresponding to a given embedding. In the
known DS reductions found to date, for which the \W-algebras are denoted by
-algebras and are called canonical, the
quasi-primary basis corresponds to the highest weights of the . Here we
find some examples of noncanonical DS reductions leading to \W-algebras which
are direct products of -algebras and `free field'
algebras with conformal weights . We also show
that if the conformal weights of the generators of a -algebra
obtained from DS reduction are nonnegative (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0
Discerning Aggregation in Homogeneous Ensembles: A General Description of Photon Counting Spectroscopy in Diffusing Systems
In order to discern aggregation in solutions, we present a quantum mechanical
analog of the photon statistics from fluorescent molecules diffusing through a
focused beam. A generating functional is developed to fully describe the
experimental physical system as well as the statistics. Histograms of the
measured time delay between photon counts are fit by an analytical solution
describing the static as well as diffusing regimes. To determine empirical
fitting parameters, fluorescence correlation spectroscopy is used in parallel
to the photon counting. For expedient analysis, we find that the distribution's
deviation from a single Poisson shows a difference between two single fluor
moments or a double fluor aggregate of the same total intensities. Initial
studies were performed on fixed-state aggregates limited to dimerization.
However preliminary results on reactive species suggest that the method can be
used to characterize any aggregating system.Comment: 30 pages, 5 figure
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