The mathematical structure of quantum real numbers
| dc.creator | Corbett, John V. | |
| dc.date | 2009-05-07 | |
| dc.date.accessioned | 2026-07-07T13:12:35Z | |
| dc.date.available | 2026-07-07T13:12:35Z | |
| dc.description | The mathematical structure of the sheaf of Dedekind real numbers $\RsubD(X)$ for a quantum system is discussed. The algebra of physical qualities is represented by an $O^{*}$ algebra $\mathcal M$ that acts on a Hilbert space that carries an irreducible representation of the symmetry group of the system. $X =\EsubS(\mathcal M)$, the state space for $\mathcal M$, has the weak topology generated by the functions $ a_{Q}(\cdot)$, defined for $\hat A \in \mathcal M_{sa} $ and $\forall \hat ρ\in \EsubS(\mathcal M) $, by $ a_{Q}(\hat ρ) = Tr \hat A \hat ρ$. For any open subset $W$ of $\EsubS(\mathcal M)$, the function $ a_{Q}|_{W}$ is the numerical value of the quality $\hat A$ defined to the extent $W$. The example of the quantum real numbers for a single Galilean relativistic particle is given. | |
| dc.description | 24 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/0905.0944 | |
| dc.identifier | http://arxiv.org/abs/0905.0944 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229622 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47L90; 32L81 | |
| dc.title | The mathematical structure of quantum real numbers | |
| dc.type | text |