ar X iv : h ep - t h / 92 06 01 3 v 1 3 J un 1 99 2 Quantum and super - quantum group related to the Alexander - Conway polynomial 1

ar X iv : h ep - t h / 93 09 02 9 v 1 6 S ep 1 99 3 Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial ∗

We discuss multivariable invariants of colored links associated with the N dimensional root of unity representation of the quantum group. The invariants for N > 2 are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When (N, 3) = 1 and N is odd, the invariant does not vanis...

ar X iv : h ep - t h / 92 04 06 8 v 1 2 3 A pr 1 99 2 CORNER TRANSFER MATRICES AND QUANTUM AFFINE

Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the antiferroelectric regime. It acts on the infinite tensor product W = V ⊗ V ⊗ V ⊗ · · ·, where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra Uq ( ŝl (2) ) . We observe that H is the derivation of Uq ( ŝl (2) ) , and conjecture that the eigenvectors of H form the level-1 vacuum re...

ar X iv : h ep - t h / 92 06 05 6 v 2 8 J ul 1 99 3 hep - th / 9206056 UCSBTH – 92 – 22 Revised July 1993 IS PURITY ETERNAL ?

Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.

ar X iv : h ep - t h / 99 06 02 9 v 1 3 J un 1 99 9

ar X iv : h ep - t h / 01 06 06 6 v 1 7 J un 2 00 1 Uniqueness of Inverse Scattering Problem in Local Quantum

It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized