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https://hdl.handle.net/2440/3456
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Type: | Journal article |
Title: | Instructions and the Information Metric |
Author: | Groisser, D. Murray, M. |
Citation: | Annals of Global Analysis and Geometry, 1997; 15(6):519-537 |
Publisher: | KLUWER ACADEMIC PUBL |
Issue Date: | 1997 |
ISSN: | 0232-704X |
Abstract: | The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian four-manifolds. Compared with the more widely known L2 metric, the information metric better reflects the conformal invariance of the self-dual Yang-Mills equations, and seems to have better completeness properties. In the case of SU(2) instantons on S4 of charge one, g is known to be the hyperbolic metric on the five-ball. We show more generally that for charge-one SU(2) instantons over 1-connected, positive-definite manifolds, g is non-degenerate and complete in the collar region of M, and is "asymptotically hyperbolic" there; g vanishes at the cone points of M. We give explicit formulae for the metric on the space of instantons of charge one on CP2. |
DOI: | 10.1023/A:1006560802410 |
Published version: | http://dx.doi.org/10.1023/a:1006560802410 |
Appears in Collections: | Aurora harvest 6 Pure Mathematics publications |
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