G_2^1 Affine Toda Field Theory: A Numerical Test of Exact S-Matrix results

We present the results of a Monte--Carlo simulation of the $G_2^{(1)}$ Affine Toda field theory action in two dimensions. We measured the ratio of the masses of the two fundamental particles as a function of the coupling constant. Our results strongly support the conjectured duality with the $D_4^{(3)}$ theory, and are consistent with the mass formula of Delius et al.Comment: 5 pages, LaTeX, DTP-9223, DAMTP-92-4

Colour valued Scattering Matrices

We describe a general construction principle which allows to add colour values to a coupling constant dependent scattering matrix. As a concrete realization of this mechanism we provide a new type of S-matrix which generalizes the one of affine Toda field theory, being related to a pair of Lie algebras. A characteristic feature of this S-matrix is that in general it violates parity invariance. For particular choices of the two Lie algebras involved this scattering matrix coincides with the one related to the scaling models described by the minimal affine Toda S-matrices and for other choices with the one of the Homogeneous sine-Gordon models with vanishing resonance parameters. We carry out the thermodynamic Bethe ansatz and identify the corresponding ultraviolet effective central charges.Comment: 8 pages Latex, example, comment and reference adde

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

International Max Planck Research Schools: Neue Wege der Graduiertenausbildung

"Die IMPRS [International Max Planck Research Schools] bilden Zentren wissenschaftlicher Exzellenz auf innovativen und interdisziplinären Forschungsgebieten, wie z.B. Neurowissenschaften oder Polymerforschung, aber auch Demografie und Bildungsforschung." Die Nachwuchsförderung findet in enger Kooperation von Universitäten und Max-Planck-Instituten statt. Es werden Promotionsstudiengänge angeboten, "die gezielt besonders qualifizierte junge Wissenschaftlerinnen und Wissenschaftler aus dem In- und Ausland in der Phase zwischen dem ersten berufsqualifizierenden Abschluss und der Promotion anziehen sollen." Die Autorinnen geben allgemeine Informationen über die IMPRS und gehen speziell auf die International Max Planck Research School "The Life Course: Evolutionary and Ontogenetic Dynamics" (LIFE) ein. Abschließend findet eine Bewertung dieser Research School statt. (DIPF/Orig./av

Quantum Conserved Currents in Supersymmetric Toda Theories

We consider $N=1$ supersymmetric Toda theories which admit a fermionic untwisted affine extension, i.e. the systems based on the $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ superalgebras. We construct the superspace Miura trasformations which allow to determine the W-supercurrents of the conformal theories and we compute their renormalized expressions. The analysis of the renormalization and conservation of higher-spin currents is then performed for the corresponding supersymmetric massive theories. We establish the quantum integrability of these models and show that although their Lagrangian is not hermitian, the masses of the fundamental particles are real, a property which is maintained by one-loop corrections. The spectrum is actually much richer, since the theories admit solitons. The existence of quantum conserved higher-spin charges implies that elastic, factorized S-matrices can be constructed.Comment: 35 pages, IFUM 426/F

From Quantum Universal Enveloping Algebras to Quantum Algebras

The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping algebra of a n-dimensional Lie algebra g=Lie(G). However, we show how, by starting from the generators of the underlying Lie bialgebra (g,\delta), the analyticity in the deformation parameter(s) allows us to determine in a unique way a set of n ``almost primitive'' basic objects in U_q(g), that could be properly called the ``quantum algebra generators''. So, the analytical prolongation (g_q,\Delta) of the Lie bialgebra (g,\delta) is proposed as the appropriate local structure of G_q. Besides, as in this way (g,\delta) and U_q(g) are shown to be in one-to-one correspondence, the classification of quantum groups is reduced to the classification of Lie bialgebras. The su_q(2) and su_q(3) cases are explicitly elaborated.Comment: 16 pages, 0 figures, LaTeX fil