Gustav W. Delius

EXACT S-MATRICES FOR NONSIMPLY-LACED AFFINE TODA THEORIES

Abstract We derive exact, factorized, purely elastic scattering matrices for the affine Toda theories based on the nonsimply-laced Lie algebras a 2 n −1 (2) , b n (1) , c c (1) , d n (2) , and g n (1) , as well as the superalgebras A (4) (0, 2 n ) and B (1) (0, n ).

Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line

Abstract: We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining property for representations of certain coideal subalgebras of Uq(ĝ).

Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.

On the Construction of Trigonometric Solutions of the Yang-Baxter Equation

We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of two irreducible representations of a quantum algebra Uq(G). Our method is a generalization of the tensor product graph method to the case of two different representations. It yields the decomposition of the R-matrix into projection operators. Many new examples of trigonometric R-matrices (solutions to the spectral parameter dependent Yang-Baxter equation) are constructed using this approach.

ON TYPE I QUANTUM AFFINE SUPERALGEBRAS

The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.

A stability analysis of the power-law steady state of marine size spectra.

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a “jump-growth” equation, a first order approximation which is the widely used McKendrick–von Foerster equation, and a second order approximation which is the McKendrick–von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick–von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick–von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

Free quantum action and BRST charge for the superparticle

Abstract We perform the covariant gauge fixing of the Brink-Schwarz superparticle action in its Batalin-Vilkovisky form in such a way that we obtain a free quantum action. We give its BRST charge.

Exact S-matrices with affine quantum group symmetry

Abstract We show how to construct the exact factorized S -matrices of 1+1 dimensional quantum field theories whose symmetry charges generate a quantum affine algebra. Quantum affine Toda theories are examples of such theories. We take into account that the Lorentz spins of the symmetry charges determine the gradation of the quantum affine algebras. This gives the S -matrices a non-rigid pole structure. It depends on a kind of “quantum” dual Coxeter number which will therefore also determine the quantum mass ratios in these theories. As an example we explicitly construct S -matrices with U q ( c n (1) ) symmetry.

The exact S-matrices of affine Toda theories based on Lie superalgebras

Abstract We determine exact S -matrices for affine Toda theories based on the Lie superalgebras A (2) (0, 2 n −1) and C (2) ( n +1). We verify that they are consistent with the tree-level amplitudes computed from the corresponding lagrangians, and that the double poles they contain are accounted for by contributions from one-loop diagrams.

The method of coadjoint orbits; An algorithm for the construction of invariant actions

The method of coadjoint orbits produces for any infinite dimensional Lie (super) algebra A with nontrivial central charge an action for scalar (super) fields which has at least the symmetry A. In this article, we try to make this method accessible to a larger audience by analyzing several examples in more detail than in the literature. After working through the Kac-Moody and Virasoro cases, we apply the method to the super Virasoro algebra and reobtain the supersymmetric extension of Polyakovs local nonpolynomial action for two-dimensional quantum gravity. As in the Virasoro case this action corresponds to the coadjoint orbit of a pure central extension. We further consider the actions corresponding to the other orbits of the super Virasoro algebra. As a new result we construct the actions for the N = 2 super Virasoro algebra.