12,452 research outputs found
The Tensor Track, III
We provide an informal up-to-date review of the tensor track approach to
quantum gravity. In a long introduction we describe in simple terms the
motivations for this approach. Then the many recent advances are summarized,
with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion,
Osterwalder-Schrader positivity...) which, while important for the tensor track
program, are not detailed in the usual quantum gravity literature. We list open
questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure
Network Models
Networks can be combined in various ways, such as overlaying one on top of
another or setting two side by side. We introduce "network models" to encode
these ways of combining networks. Different network models describe different
kinds of networks. We show that each network model gives rise to an operad,
whose operations are ways of assembling a network of the given kind from
smaller parts. Such operads, and their algebras, can serve as tools for
designing networks. Technically, a network model is a lax symmetric monoidal
functor from the free symmetric monoidal category on some set to
, and the construction of the corresponding operad proceeds via a
symmetric monoidal version of the Grothendieck construction.Comment: 46 page
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