A New Approach to Quantising Space-Time: I. Quantising on a General Category
| dc.creator | Isham, C. J. | |
| dc.date | 2003-03-17 | |
| dc.date | 2003-12-24 | |
| dc.date.accessioned | 2026-07-25T17:06:03Z | |
| dc.description | A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose `configuration space' (or history-theory analogue) can be regarded as the set of objects in a category. In this first of a series of papers, we study this question in general and develop a scheme based on constructing an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold $Q\simeq G/H$ where G and H are Lie groups. In particular, we choose as the analogue of G the monoid of `arrow fields' on the category. Physically, this means that an arrow between two objects in the category is viewed as some sort of analogue of momentum. After finding the `category quantisation monoid', we show how suitable representations can be constructed using a bundle of Hilbert spaces over the set of objects. | |
| dc.description | Latex2e | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0303060 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0303060 | |
| dc.identifier | Adv.Theor.Math.Phys. 7 (2003) 331-367 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/45742 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Physics | |
| dc.title | A New Approach to Quantising Space-Time: I. Quantising on a General Category | |
| dc.type | text |