A New Approach to Quantising Space-Time: III. State Vectors as Functions on Arrows

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dc.creatorIsham, C. J.
dc.date2003-06-16
dc.date.accessioned2026-07-07T03:27:55Z
dc.date.available2026-07-07T03:27:55Z
dc.descriptionIn two recent papers by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects, $\Ob\Q$, in a (small) category $\Q$. The quantum states in this approach are cross-sections of a bundle $A\leadsto\K[A]$ of Hilbert spaces over $\Ob\Q$. The Hilbert spaces $\K[A]$, $A\in\Ob\Q$, depend strongly on the object $A$, and have to be chosen so as to get an irreducible, faithful, representation of the basic `category quantisation monoid'. In the present paper, we develop a different approach in which the state vectors are complex-valued functions on the set of {\em arrows} in $\Q$. This throws a new light on the Hilbert bundle scheme: in particular, we recover the results of that approach in the, physically important, example when $\Q$ is a small category of finite sets.
dc.descriptionLatex2e
dc.identifierhttps://arxiv.org/abs/gr-qc/0306064
dc.identifierhttp://arxiv.org/abs/gr-qc/0306064
dc.identifierAdv.Theor.Math.Phys. 8 (2004) 797-811
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34623
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleA New Approach to Quantising Space-Time: III. State Vectors as Functions on Arrows
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