Classical and Quantum Fermions Linked by an Algebraic Deformation
| dc.creator | Mostafazadeh, Ali | |
| dc.date | 2003-12-24 | |
| dc.date.accessioned | 2026-07-07T06:24:28Z | |
| dc.date.available | 2026-07-07T06:24:28Z | |
| dc.description | We study the regular representation $ρ_ζ$ of the single-fermion algebra ${\cal A}_ζ$, i.e., $c^2=c^{+2}=0$, $cc^++c^+c=ζ~1$, for $ζ\in [0,1]$. We show that $ρ_0$ is a four-dimensional nonunitary representation of ${\cal A}_0$ which is faithfully irreducible (it does not admit a proper faithful subrepresentation). Moreover, $ρ_0$ is the minimal faithfully irreducible representation of ${\cal A}_0$ in the sense that every faithful representation of ${\cal A}_0$ has a subrepresentation that is equivalent to $ρ_0$. We therefore identify a classical fermion with $ρ_0$ and view its quantization as the deformation: $ζ:0\to 1$ of $ρ_ζ$. The latter has the effect of mapping $ρ_0$ into the four-dimensional, unitary, (faithfully) reducible representation $ρ_1$ of ${\cal A}_1$ that is precisely the representation associated with a Dirac fermion. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0312065 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0312065 | |
| dc.identifier | Int. J. Geom. Meth. Mod. Phys. 2, 777-782 (2005) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96552 | |
| dc.subject | Mathematical Physics | |
| dc.title | Classical and Quantum Fermions Linked by an Algebraic Deformation | |
| dc.type | text |