Classical and Quantum Fermions Linked by an Algebraic Deformation

Details Classical and Quantum Fermions Linked by an Algebraic Deformation Classical and Quantum Fermions Linked by an Algebraic Deformation

2003-12-24

arxiv.org/abs/math-ph/0312065v1

Int. J. Geom. Meth. Mod. Phys. 2, 777-782 (2005)

Physics

Mathematical Physics

7 pages

Scientific paper

We study the regular representation $\rho_\zeta$ of the single-fermion algebra ${\cal A}_\zeta$, i.e., $c^2=c^{+2}=0$, $cc^++c^+c=\zeta~1$, for $\zeta\in [0,1]$. We show that $\rho_0$ is a four-dimensional nonunitary representation of ${\cal A}_0$ which is faithfully irreducible (it does not admit a proper faithful subrepresentation). Moreover, $\rho_0$ 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 $\rho_0$. We therefore identify a classical fermion with $\rho_0$ and view its quantization as the deformation: $\zeta:0\to 1$ of $\rho_\zeta$. The latter has the effect of mapping $\rho_0$ into the four-dimensional, unitary, (faithfully) reducible representation $\rho_1$ of ${\cal A}_1$ that is precisely the representation associated with a Dirac fermion.

Affiliated with

Also associated with

No associations

Rating

Classical and Quantum Fermions Linked by an Algebraic Deformation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical and Quantum Fermions Linked by an Algebraic Deformation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical and Quantum Fermions Linked by an Algebraic Deformation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640855