Representations of the Rotationally Invariant Algebra of Quantum Spin Systems.
Abstract
An algebra of all observables associated with quantum spin systems is investigated as the simplest nontrivial model of a nonabelian gauge invariant discrete quantum field theory. The quantum spin systems considered are restricted to systems which consist of particles of spin 1/2 situated at each lattice site. The observables at each lattice site are composed of the spin operators which are represented by Pauli spin matrices. The rotationally invariant (RINV) algebra is highlighted. The RINV algebra is obtained as the restriction to the subalgebra of the lattice algebra which is invariant under the rotation of the lattice as a whole. The structure of the RINV algebra is presented and its connection with the symmetric group is stated.
 Publication:

Ph.D. Thesis
 Pub Date:
 1979
 Bibcode:
 1979PhDT........78S
 Keywords:

 Physics: General;
 Algebra;
 Gauge Invariance;
 Particle Spin;
 Quantum Theory;
 Lattices (Mathematics);
 Mathematical Models;
 Operators (Mathematics);
 Thermodynamics and Statistical Physics