The structure of the observable algebra determined by a Hopf *-subalgebra in Hopf spin models

Let H be a finite dimensional Hopf C*-algebra, H1 a Hopf*-subalgebra of H. This paper focuses on the observable algebra AH1 determined by H1 in nonequilibrium Hopf spin models, in which there is a copy of H1 on each lattice site, and a copy of ? on each link, where ? denotes the dual of H. Furthermore, using the iterated twisted tensor product of finite +*-algebras, one can prove that the observable algebraAH1 is *-isomorphic to the C*-inductive limit ... o H1 o ? o H1 o ? o H1 o ... .

Jones Type Basic Construction on Hopf Spin Models

Let H be a finite dimensional C∗-Hopf algebra and A the observable algebra of Hopf spin models. For some coaction of the Drinfeld double D(H) on A, the crossed product A⋊D(H)^ can define the field algebra F of Hopf spin models. In the paper, we study C∗-basic construction for the inclusion A⊆F on Hopf spin models. To achieve this, we define the action α:D(H)×F→F, and then construct the resulting crossed product F⋊D(H), which is isomorphic A⊗End(D(H)^). Furthermore, we prove that the C∗-basic construction for A⊆F is consistent to F⋊D(H), which yields that the C∗-basic constructions for the inclusion A⊆F is independent of the choice of the coaction of D(H) on A.

GAUGE ALGEBRA OF IRREDUCIBLE THEORIES IN THE Sp(2)-SYMMETRIC BRST FORMALISM

An explicit solution to classical master equations of the Sp(2)-symmetric Hamiltonian BRST quantization scheme is presented in the case of irreducible gauge theories. A realization of the observable algebra is constructed.

WHITE NOISE HEISENBERG EVOLUTION AND EVANS–HUDSON FLOWS

We study white noise Heisenberg equations giving rise to flows which are *-automorphisms of the observable algebra, but not necessarily inner automorphisms. We prove that the causally normally ordered form of these white noise Heisenberg equations are equivalent to Evans–Hudson flows. This gives in particular, the microscopic structure of the maps defining these flows, in terms of the original white noise derivations.

CHIRAL DECOMPOSITION AS A SOURCE OF QUANTUM SYMMETRY IN THE ISING MODEL

The superselection sectors of three closely related models are studied and compared. I. The full Ising model with observable algebra [Formula: see text], the universal algebra of local even CAR algebras on the circle. [Formula: see text] has four sectors with Z(2) × Z(2) symmetry. II. The chiral Ising model with observable algebra [Formula: see text] (c = L or R), which is the universal algebra of local even Majorana algebras, has three sectors with quantum symmetry Gc ≅ M1⊕M1⊕M2. The Mack-Schomerus endomorphism creating the non-Abelian sector of [Formula: see text], respectively of [Formula: see text] is shown to coincide with the restriction [Formula: see text], respectively [Formula: see text] of a Z (2) charge creating automorphism ρ of [Formula: see text]. III. As an intermediate step the superselection sectors of the algebra [Formula: see text] — which can be interpreted as the observable algebra of the conformal Ising model — are found to have ordinary group symmetry described by the dihedral group D4. The relation between the sectors of [Formula: see text] and [Formula: see text] is explained in terms of a strange 'symmetry breaking': symmetry enhancement in the Neveu-Schwarz sector and symmetry breaking in the Ramond. Covariant charged fields are constructed in all three cases and the truncation in Gc is shown to arise from the failure of the Cuntz algebra relations for the chiral charged fields.