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This article is cited in 7 scientific papers (total in 7 papers)
Selective Categories and Linear Canonical Relations
David Li-Bland, Alan Weinstein Department of Mathematics, University of California, Berkeley, CA 94720 USA
Abstract:
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are “good”. We then apply this notion to the category $\mathbf{SLREL}$ of linear canonical relations and the result ${\rm WW}(\mathbf{SLREL})$ of our version of the WW construction, identifying the morphisms in the latter with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in $\mathbf{SLREL}$ itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts.
Keywords:
symplectic vector space; canonical relation; rigid monoidal category; highly selective category; quantization.
Received: July 22, 2014; in final form October 20, 2014; Published online October 26, 2014
Citation:
David Li-Bland, Alan Weinstein, “Selective Categories and Linear Canonical Relations”, SIGMA, 10 (2014), 100, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma965 https://www.mathnet.ru/eng/sigma/v10/p100
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Abstract page: | 267 | Full-text PDF : | 29 | References: | 22 |
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