Nonstandard coproducts and the Izergin-Korepin open spin chain

Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using these R and K matrices, one can construct transfer matrices for open integrable quantum spin chains. The transfer matrix corresponding to the identity matrix K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer matrices corresponding to the other two K matrices also have U_q(o(3)) symmetry, but with a nonstandard coproduct. We briefly explore some of the consequences of this symmetry.Comment: 7 pages, LaTeX; v2 has one additional sentence on the degeneracy patter

Analytical Bethe Ansatz for A2n−1(2),Bn(1),Cn(1),Dn(1)A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n quantum-algebra-invariant open spin chains

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras $A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n$, and which have the quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$, respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is removed

Boundary K-matrices for the XYZ, XXZ AND XXX spin chains

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.Comment: 13 page

Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps

Classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate $\hbar$-independent quantum canonical maps. It is shown that such maps act in the noncommutative phase space as dictated by the classical covariance. A crucial observation made is that under the classical covariance the local quantum mechanical picture can become nonlocal in the Hilbert space. This nonlocal picture is made equivalent by the Weyl map to a noncommutative picture in the phase space formulation of the theory. The connection between the entanglement and nonlocality of the representation is explored and specific examples of the generation of entanglement are provided by using such concepts as the generalized Bell states. That the results have direct application in generating vacuum soliton configurations in the recently popular scalar field theories of noncommutative coordinates is also demonstrated.Comment: 14 pages, one figur

Twistors and the massive spinning particle

Gauge-invariant twistor variables are found for the massive spinning particle with N-extended local worldline supersymmetry, in spacetime dimensions D = 3, 4, 6. The twistor action is manifestly Lorentz invariant but the anticommuting spin variables appear exactly as in the non-relativistic limit. This allows a simple confirmation that the quantum N = 2 spinning particle has either spin one or spin zero, and that N > 2 is quantum inconsistent for D = 4, 6.LM acknowledges partial support from the National Science Foundation Award PHY-1214521. PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society, and he thanks the University of Groningen for hospitality during the writing of this paper. LM and PKT are grateful for the hospitality of the Pedro Pascual Benasque Center for Science, where part of this work was done.This is the final version of the article. It first appeared from IOP via http://dx.doi.org/10.1088/1751-8113/49/2/02540

Quantum 3D Superstrings

The classical Green-Schwarz superstring action, with N=1 or N=2 spacetime supersymmetry, exists for spacetime dimensions D=3,4,6,10, but quantization in the light-cone gauge breaks Lorentz invariance unless either D=10, which leads to critical superstring theory, or D=3. We give details of results presented previously for the bosonic and N=1 closed 3D (super)strings and extend them to the N=2 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.Comment: 46 pages, v5 corrects more typos and minor error

The XX--model with boundaries. Part I: Diagonalization of the finite chain

This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction

Simplified Calculation of Boundary S Matrices

The antiferromagnetic Heisenberg spin chain with N spins has a sector with N=odd, in which the number of excitations is odd. In particular, there is a state with a single one-particle excitation. We exploit this fact to give a simplified derivation of the boundary S matrix for the open antiferromagnetic spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.Comment: 8 pages, LaTeX, no figure

Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions

An integrable version of the supersymmetric t-J model which is quantum group invariant as well as periodic is introduced and analysed in detail. The model is solved through the algebraic nested Bethe ansatz method.Comment: 11 pages, LaTe

The Supersymmetric t-J Model with a Boundary

An open supersymmetric t-J chain with boundary fields is studied by means of the Bethe Ansatz. Ground state properties for the case of an almost half-filled band and a bulk magnetic field are determined. Boundary susceptibilities are calculated as functions of the boundary fields. The effects of the boundary on excitations are investigated by constructing the exact boundary S-matrix. From the analytic structure of the boundary S-matrices one deduces that holons can form boundary bound states for sufficiently strong boundary fields.Comment: 23 pages of revtex, discussion on analytic structure of holon S-matrix change