A local and integrable lattice regularization of the massive Thirring model

The light-cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice hamiltonian written in terms of discrete Fermi fields. Several subtle points concerning boundary conditions, normal ordering, continuum limit, finite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six-vertex anisotropy and the various coupling constants of the continuum are analyzed in detail.     

Expectation values of local fields in the Bullough-Dodd model and integrable perturbed conformal field theories

Exact expectation values of the fields e^aϕ in the Bullough-Dodd model are derived by adopting the “reflection relations” which involve the reflection S-matrix of the Liouville theory, as well as a special analyticity assumption. Using this result we propose explicit expressions for expectation values of all primary operators in the c < 1 minimal CFr perturbed by the operator φ_1,2 or φ_2,1. Some results concerning the φ_1,5 perturbed minimal models are also presented.     

Hidden local gauge invariance in integrable magnetic chains

It is shown that local gauge transformations preserve the integrability of one-dimensional quantum Heisenberg chains. Abelian U(1) gauge transformations associated to z-rotations appear in the XXZ model which is worked out in detail. The exact energy spectrum derived by the Bethe ansatz turns out to be gauge-invariant whereas the eigenvectors are explicitly gauge-dependent. Isotropic XXX chains exhibit SU(2) ⊗ Z₂ gauge invariance properties and anisotropic XYZ chains possess discrete Z₂ ⊗ Z₂ gauge invariance.     

Type-I integrable quantum impurities in the Heisenberg model

Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.     

A generalized SHGI integrable hierarchy and its expanding integrable model

An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered.     

An integrable model in general relativity

Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov exponent calculations for a two-well Duffing oscillator. Received 21 May 2002 / Received in final form 13 September 2002 Published online 29 November 2002     

Poincaré partially integrable local representations and mass-spectrum

An example is given of an irreducible representation of a finite-dimensional Lie algebra containing the Poincaré Lie algebra and giving rise to isolated positive masses. In addition the representation is Poincaré partially integrable (which assures the continuous physical spectrum for the energy- momentum vector) and Poincaré-covariant in a weak sense.A connection between this example and some recently published impossibility theorems is shown, and conclusions about a possible future work in this domain are also drawn.     

Boundary Yang-Baxter equation in the RSOS/SOS representation

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and nondiagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins, respectively. Applied to (1 + 1)-dimensional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.     

BCS–BEC crossover in one-dimensional integrable model

The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.     

Solvable RSOS models based on the dilute BWM algebra

In this paper we present representations of the recently introduced dilute Birman-Wenzl-Murakami algebra. These representations, labelled by the level-l B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ affine Lie algebras, are baxterized to yield solutions to the Yang-Baxter equation. The thus obtained critical solvable models are RSOS counterparts of the, respectively, D_n+1⁽²⁾, A_2n⁽²⁾ and B_n⁽¹⁾R-matrices of Bazhanov and Jimbo. For the D_n+1⁽²⁾ and B_n⁽¹⁾ algebras the RSOS models are new. An elliptic extension which solves the Yang-Baxter equation is given for all three series of dilute RSOS models.     

Transition amplitudes and probabilities for the Weinberg-Salam model

Transition probabilities for the processes vv?vv, vv?, $\text{vv}$?$\text{vv}$, and spin-dependent transition amplitudes for the processes ve?ve, vē?vē, v?e?v?e, $\text{ve}$?$\text{ve}$ and vv??eē are calculated in lowest order for the Weinberg-Salam model.     

Shape changing and accelerating solitons in the integrable variable mass sine-gordon model

The sine-Gordon model with a variable mass (VMSG) appears in many physical systems, ranging from the current through a nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or perturbatively. We construct a class of VMSG models, integrable at both the classical and the quantum levels with exact soliton solutions, which can accelerate and change their shape, width, and amplitude simulating realistic inhomogeneous systems at certain limits.     

Exact form factors in integrable quantum field theories: the sine-Gordon model

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of ‘maximal analyticity” and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the “off-shell” Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three-particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.     

On a integrable deformations of Heisenberg supermagnetic model

The Heisenberg supermagnet model which is the supersymmetric generalization of the Heisenberg ferromagnet model is an important integrable system. We consider the deformations of Heisenberg supermagnet model under the two constraint 1. S² = S for S ∈ USPL(2/1)/S(L(1/1) × U(1)) and 2. S² = 3S ? 2I S ∈ USPL(2/1)/S(U(2) × U(1)). By means of the gauge transformation, we construct the gauge equivalent counterparts, i.e., the super generalized Hirota equation and Gramman odd nonlinear Schrödinger equation.     

Higher quantum conserved current in a new completely integrable model

The first higher local quantum conserved current in the recently proposed new completely integrable (2 e+e^-2)₂ model is explicitly constructed thus proving absence of particle production and factorization of multiparticle scattering.     

Dynamics of a light field in a composite integrable model

The inverse scattering transform method is used to solve the model that describes the evolution of light pulses in an optical system that includes a set of media with different nonlinear optical properties. As a physical example, we analyze a model composed of the systems of equations that describe the resonant interaction of a very short light pulse with an energy transition of the medium and the ensuing propagation of the light field in an optical fiber. The constant boundary value of one of the fields is shown to result in an asymptotic quasi-radiative solution of the model.