Hidden supersymmetry of a $P,T-$invariant $3D$ fermion system

Details Hidden supersymmetry of a $P,T-$invariant $3D$ fermion system Hidden supersymmetry of a $P,T-$invariant $3D$ fermion system

1995-11-04

arxiv.org/abs/hep-th/9511028v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, LaTeX

Scientific paper

We show that a (2+1)-dimensional $P,T-$invariant free fermion system, relevant to $P,T-$conserving models of high-$T_c$ superconductivity, has a U(1,1) dynamical symmetry as well as an $N=3$ supersymmetry with the even generator being a quadratic function of the spin operator and of the generator of chiral ${\rm U_c(1)}$ transformations. We demonstrate that the hidden supersymmetry leads to a non-standard superextension of the (2+1)-dimensional Poincar\'e group. As a result, the one particle states of the $P,T-$invariant fermion system realize an irreducible representation of the Poincar\'e supergroup labelled by the zero eigenvalue of the superspin operator.

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