Wilson Brenna, Cecilia Flori
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doring, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions. In recent years the topic has been con- siderably progressing with the introduction of probabilities, group and group transformations. In the present paper we will introduce a candidate for the complex quantity value object and analyse its relation to the real quantity value object. By defining the Grothendieck k-extension of these two objects, so as to turn them into abelian groups, it is possible to define internal one parameter groups in a topos. The idea is that such groups will eventually enable us to define the topos analogue of a KMS state.
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http://arxiv.org/abs/1206.0809
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