Altering the Symmetry of Wavefunctions in Quantum Algebras and Supersymmetry

The statistics-altering operators present in the limit $q=-1$ of multiparticle SU_q(2)-invariant subspaces parallel the action of such operators which naturally occur in supersymmetric theories. We illustrate this heuristically by comparison to a toy $N=2$ superymmetry algebra, and ask whether there is a supersymmetry structure underlying SU(2)_q at that limit. We remark on the relevance of such alternating-symmetry multiplets to the construction of invariant hamiltonians.Comment: 6 page

INJECT: Algorithms to Discover Creative Angles on News

INJECT is a new digitaltool tosupport journalists to think more creativelywhendiscoveringnewangles on stories under devel-opment. It deliversinteractiveand intelligentsupport embeddedin the text editorsthat journalists work with regularly. This support is generated bycombiningcomplex creative searchesofmillionsof related news storiespublished in multiplelanguageswith entityextraction algorithms and interactive creative guidance tailored to news. This paper reportsthetool’sarchitecture, some itsalgo-rithms, and the design decisions made to delivera reliable and us-able tool for journalistsin different newsroomsand work contexts

Dimensional Deconstruction and Wess-Zumino-Witten Terms

A new technique is developed for the derivation of the Wess-Zumino-Witten terms of gauged chiral lagrangians. We start in D=5 with a pure (mesonless) Yang-Mills theory, which includes relevant gauge field Chern-Simons terms. The theory is then compactified, and the effective D=4 lagrangian is derived using lattice techniques, or ``deconstruction,'' where pseudoscalar mesons arise from the lattice Wilson links. This yields the WZW term with the correct Witten coefficient by way of a simple heuristic argument. We discover a novel WZW term for singlet currents, that yields the full Goldstone-Wilczek current, and a U(1) axial current for the skyrmion, with the appropriate anomaly structures. A more detailed analysis is presented of the dimensional compactification of Yang-Mills in D=5 into a gauged chiral lagrangian in D=4, heeding the consistency of the D=4 and D=5 Bianchi identities. These dictate a novel covariant derivative structure in the D=4 gauge theory, yielding a field strength modified by the addition of commutators of chiral currents. The Chern-Simons term of the pure D=5 Yang-Mills theory then devolves into the correct form of the Wess-Zumino-Witten term with an index (the analogue of N_{colors}=3) of N=D=5. The theory also has a Skyrme term with a fixed coefficient.Comment: 29 pages, no figures; replacement fixes a typographical minus sign error in eq.(16), an errant normalization factor, and clarifies some discussion issue

Umbral Vade Mecum

In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones appearing in most areas of physics and engineering --- as maps of well-known continuous functions. This correspondence deftly sidesteps the use of more traditional methods to solve these difference equations. The umbral framework is discussed and illustrated here, with special attention given to umbral counterparts of the Airy, Kummer, and Whittaker equations, and to umbral maps of solitons for the Sine-Gordon, Korteweg--de Vries, and Toda systems.Comment: arXiv admin note: text overlap with arXiv:0710.230

Deformation Quantization of Nambu Mechanics

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved most naturally, as illustrated on nonlinear $\sigma$-models, specifically for Chiral Models and de Sitter $N$-spheres. Classically, the dynamics of superintegrable models such as these is automatically also described by Nambu Brackets involving the extra symmetry invariants of them. The phase-space quantization worked out then leads to the quantization of the corresponding Nambu Brackets, validating Nambu's original proposal, despite excessive fears of inconsistency which have arisen over the years. This is a pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points of interpretation and care needed in appreciating the consistency of Quantum Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see T Curtright's contribution in these Proceedings [hep-th 0303088].Comment: Invited talk by the first author at the Coral Gables Conference (C02/12/11.2), Ft Lauderdale, Dec 2002. 14p, LateX2e, aipproc, amsfont

Quantum Mechanics in Phase Space

Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.Comment: A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theor