12289422
Non-critical string pentagon equations and their solutions
We derive pentagon-type relations for the three-point boundary tachyon correlation functions in the non-critical open string theory with generic cmatter < 1 and study their solutions in the case of Fateev–Zamolodchikov–Zamolodchikov branes. A new general formula for the Liouville boundary three-point factor corresponding to degenerate matter is derived.
3223149
Chiral zero modes of the SU(n) WZNW model
We define the chiral zero modes’ phase space of the G = SU(n) Wess-Zumino-Novikov-Witten (WZNW) model as an (n − 1)(n + 2)dimensional manifold Mq equipped with a symplectic form Ωq involving a Wess-Zumino (WZ) term ρ which depends on the monodromy M and is implicitly defined (on an open dense neighbourhood of the group unit) by dρ(M) = 1 3 tr (MdM) . (∗) This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into an Uq(sln) symmetry for q a primitive even root of 1 . For each (non-degenerate, constant) solution of the classical Yang-Baxter equation (CYBE) we write down explicitly a ρ(M) satisfying Eq.(∗) and invert the form Ωq , thus computing the Poisson bivector of the system. The resulting Poisson brackets (PB) appear as the classical counterpart of the exchange relations of the quantum matrix algebra studied previously in [31]. We argue that it is advantageous to equate the determinant D of the zero modes’ matrix (aα) to a pseudoinvariant under permutations polynomial in the SU(n) weights, rather than to adopt the familiar convention D = 1 . A finite dimensional ”Fock space” operator realization of the factor algebra Mq/Ih , where Ih is an appropriate ideal in Mq for qh = −1 , is briefly discussed.
16434321
Operator realization of the SU(2) WZNW model
Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables M and M. Earlier work on the subject, which traced back the quantum group symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic form, left some open questions: 
• 
- How to reconcile the necessity to set MM−1 = 1 (in order to recover the monodromy invariance of the local 2D group valued field g = uu) with the fact the M and M obey different exchange relations? 
 
• 
- What is the status of the quantum symmetry in the 2D theory in which the chiral fields u(x−t) and u(x + t) commute? 
 
• 
- Is there a consistent operator formalism in the chiral (and the extended 2D) theory in the continuum limit? 
 
 
 
 
We propose a constructive affirmative answer to these questions for G = SU(2) by presenting the quantum fields u and u as sums of products of chiral vertex operators and q-Bose creation and annihilation operators.
120723238
Generalized Euler angles as intrinsic coordinates for nonlinear spinors
Among the nonlinear spinor representations of the pseudo‐orthogonal rotation groups presented in a preceding work, those ones are considered, whose carrier spaces are isomorphic with group spaces. The general element of such groups is written as a product of one‐parameter subgroups, allowing, for the SO(ν,ν) and SO(ν+1,ν) cases, to write explicitly the nonlinear spinor components in terms of independent intrinsic coordinates satisfying the Cartan’s quadratic constraints.
124797224
Dimensions for conformal spinors
SummaryThe notion of dimension for conformal spinor fields is reanalysed, with special emphasis on the relation occurring between dilatations inM3,1 andSO4,2 rotations inM4,2. Necessary and sufficient conditions for scale invariance of some Lagrangians, describing eight-componentSO4,2 spinor fields inM4,2, are given. New homogeneity conditions forSO4,2 spinor fields are proposed in order to obtain in Minkowski space a scale-invariant Dirac-like Lagrangian for a doublet of canonical four-component spinor fields.RiassuntoSi analizza la nozione di dimensione per campi spinoriali conformi, con speciale riguardo alla relazione che intercorre fra dilatazioni inM3,1 e rotazioni diSO4,2 inM4,2. Si danno condizioni necessarie e sufficienti per l’invarianza di scala di alcuni lagrangiani, descriventi campi spinoriali diSO4,2 ad otto componenti inM4,2. Si propongono nuove condizioni di omogeneità per i campi spinoriali diSO4,2 allo scopo di ottenere nello spazio di Minkowski un lagrangiano invariante di scala del tipo di Dirac per un doppietto di campi spinoriali canonici a quattro componenti.РезюмеЗаново анализируется понятие размерностм для конформных спинорных оояей, причем, особое внимание уделяется соотношению между расширениями вM3,1 иSO4,2 вращениями вM4,2. Приводятся необходимые и достаточные условия для масштабной инвариантности некоторых Лагранжианов, описывающих восьми-компонентныеSO4,2 спинорные поля вM4,2. Предлатаются новые условия однородности дляSO4,2 спинорных полей, чтобы получить в пространстве Минковского масштабно-инвариантный Лагранжиан, дираковското типа, для дублета канонических четырех-компонентных спинорных полей.
120683606
Exchange relations and correlation functions for a quantum particle on the SU2 group manifold
The SO4 invariant quantum dynamics of a point particle moving on the 3 sphere (or equivalently, of the relative motion of the spherical top) is considered. Quantum exchange relations for different times are derived with an ‘‘R matrix’’ depending on the time difference and on the conserved angular momentum. Their implications for correlation functions are spelled out. The chiral exchange relations of Alekseev and Faddeev [Commun. Math. Phys. 141, 413–422 (1991)] are also extended to different times.
199514134
SURVEY AND ALIGNMENT FOR THE SYNCHROTRON LIGHT SOURCE ELETTRA
ELETTRA is a third generation light Source currently under construction in Trieste, Italy, which will be commissioned in 1993. As a high brilliance machine, ELETTRA is designed for extremely small emittance, which causes a high sensitivity to alignment errors. First results and the general alignment method, as well as the instruments, survey tools and applied software, are described.