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Quantization Commutes with Reduction on Compact Lie Groups under the Adjoint Action

thesis
posted on 2017-06-21, 00:00 authored by Benjamin Lewis

Over the last half-century mathematicians and physicists alike have done quite a bit of work on the problem of quantization commutes with reduction and its generalizations. It turns out that in general quantization commutes with reduction, but only weakly; that is the map between the first-quantized-then-reduced space and the first-reduced-then-quantized space is only a vector isomorphism, not necessarily unitary and therefore respecting the physically relevant inner product. In this dissertation we use the techniques developed by Hall and Kirwin to show that if our starting manifold is a compact, simply connected Lie group under the adjoint action, then the map we get is, in fact, unitary.

History

Date Created

2017-06-21

Date Modified

2019-02-20

Defense Date

2017-06-21

Research Director(s)

Brian C. Hall

Committee Members

Sam Evens Richard Hind Stephan Stolz

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Program Name

  • Mathematics

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