Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 5

A New Approach to Quantising Systems: II. Quantising on a Category of Sets

Pages: 807 – 829

DOI: http://dx.doi.org/10.4310/ATMP.2003.v7.n5.a3

Author

C.J. Isham

Abstract

In [1], a new approach was suggested for finding quantum structures that might, in particular, be used in potential approaches to quantum gravity that involve non-manifold models for space and/or space-time (for example, causal sets). This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in a (small) category Q. In the present paper, we show how this theory can be applied to the special case when Q is a category of sets.

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