Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Boosting the tree augmented naive bayes classifier

The Tree Augmented Naïve Bayes (TAN) classifier relaxes the sweeping independence assumptions of the Naïve Bayes approach by taking account of conditional probabilities. It does this in a limited sense, by incorporating the conditional probability of each attribute given the class and (at most) one other attribute. The method of boosting has previously proven very effective in improving the performance of Naïve Bayes classifiers and in this paper, we investigate its effectiveness on application to the TAN classifier.