Index Theory, Gerbes, and Hamiltonian Quantization

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field.Comment: 16 pages, Plain TeX inputting AMSTe

Interview with Carey A. Moore, December 30, 2003

Carey A. Moore was interviewed on December 30, 2003 by Michael Birkner about his experiences after leaving Gettysburg College and moving on ultimately toward a Ph.D and then a teaching career. Length of Interview: 94 minutes Collection Note: This oral history was selected from the Oral History Collection maintained by Special Collections & College Archives. Transcripts are available for browsing in the Special Collections Reading Room, 4th floor, Musselman Library. GettDigital contains the complete listing of oral histories done from 1978 to the present. To view this list and to access selected digital versions please visit -- http://gettysburg.cdmhost.com/cdm/landingpage/collection/p16274coll

Orthogonal multiplexing techniques for switching in a digital local telephone exchange

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Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised version - only change a lot of irritating typos remove

The caloron correspondence and higher string classes for loop groups

We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $\Omega G$-bundles on $M$, where $\Omega G$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $\Omega G$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.Comment: 21 pages. Author addresses adde

The basic bundle gerbe on unitary groups

We consider the construction of the basic bundle gerbe on SU(n) introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n), diagonal tori and the Banach Lie group of unitary operators differing from the identity by an element of a Schatten ideal. In all these cases we give an explicit connection and curving on the basic bundle gerbe and calculate the real Dixmier-Douady class. Extensive use is made of the holomorphic functional calculus for operators on a Hilbert space