Alan L. Carey

Bio: Alan L. Carey is an academic researcher from Australian National University. The author has contributed to research in topics: Von Neumann algebra & Gerbe. The author has an hindex of 39, co-authored 215 publications receiving 4541 citations. Previous affiliations of Alan L. Carey include University of Wollongong & University of Adelaide.

Twisted K-theory and K-Theory of Bundle Gerbes

Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of K-brane charges in nontrivial backgrounds are briefly discussed.

Systems science and systems thinking for public health: a systematic review of the field.

Abstract: Objectives: This paper reports on findings from a systematic review designed to investigate the state of systems science research in public health. The objectives were to: (1) explore how systems methodologies are being applied within public health and (2) identify fruitful areas of activity. Design: A systematic review was conducted from existing literature that draws on or uses systems science (in its various forms) and relates to key public health areas of action and concern, including tobacco, alcohol, obesity and the social determinants of health. Data analysis: 117 articles were included in the review. An inductive qualitative content analysis was used for data extraction. The following were systematically extracted from the articles: approach, methodology, transparency, strengths and weaknesses. These were then organised according to theme (ie, commonalities between studies within each category), in order to provide an overview of the state of the field as a whole. The assessment of data quality was intrinsic to the goals of the review itself, and therefore, was carried out as part of the analysis. Results: 4 categories of research were identified from the review, ranging from editorial and commentary pieces to complex system dynamic modelling. Our analysis of each of these categories of research highlighted areas of potential for systems science to strengthen public health efforts, while also revealing a number of limitations in the dynamic systems modelling being carried out in public health. Conclusions: There is a great deal of interest in how the application of systems concepts and approach might aid public health. Our analysis suggests that soft systems modelling techniques are likely to be the most useful addition to public health, and align well with current debate around knowledge transfer and policy. However, the full range of systems methodologies is yet to be engaged with by public health researchers.

Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

Abstract: We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H4(BG, ℤ) for a compact semi-simple Lie group G. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Chern-Simons functionals and Wess-Zumino-Witten models associated to the group G. We do this by introducing a lifting to the level of bundle gerbes of the natural map from H4(BG, ℤ) to H3(G, ℤ). The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non-simply connected Lie groups. The implications for Wess-Zumino-Witten models are also discussed.

On fermion gauge groups, current algebras and Kac-Moody algebras

Abstract: Representations of groups of loops in U(N), SO(N) and various subgroups are studied. The representations are defined on fermion Fock spaces, and may be regarded as local gauge groups in the context of the two-dimensional many-particle Dirac theory for charged or neutral particles with rest mass m/> 0. For m = 0, the representations are shown to give rise to type I® factors, while for m > 0 hyperfinite, type III~ factors arise. A key point in the structure analysis is a convergence result: We prove that suitably rescaled representers of certain nonzero winding number loops converge to the free Dirac fields. We also present applications to cyclicity and irreducibility questions concerning the Dirac currents, and to the representation theory of a class of Kac-Moody Lie algebras.

Table Of Integrals Series And Products

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Methods Of Modern Mathematical Physics

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Complete integrability of relativistic Calogero-Moser systems and elliptic function identities

Abstract: Poincare-invariant generalizations of the Galilei-invariant Calogero-Moser AΓ-particle systems are studied. A quantization of the classical integrals S1?...,SN is presented such that the operators Si9...,SN mutually commute. As a corollary it follows that Si9...9SN Poisson commute. These results hinge on functional equations satisfied by the Weierstrass σ- and 0*- functions. A generalized Cauchy identity involving the σ-function leads to an N x N matrix L whose symmetric functions are proportional to Sl5 ...9SN.