121493629
Minimal surfaces and strings from spinors a realization of the cartan programme
SummaryIt is shown ow the old Enneper-Weierstrass integral parametrization ofminimal surfaces inR3 and the Eisenhart ones inR3,1, when expressed through bilinear spinor polynomia, may be considered as deriving from a particularlocal realization of the possibility envisaged by Cartan: to consider ordinary vectors as generated from isotropic planes in complex spaces, in the frame of the bijective Cartan map connecting pure spinor directions to totally null planes in complex spaces. In the case ofR3 the correspondingglobal realization of the Cartan map extends the Enneper-Weierstrass parametrization to the Gauss-conformal map of the minimal surface to S2, which may be identified with the Riemann celestial sphere. Forreal spinors minimal surfaces are substituted bystrings both inR2,1 andR3,1; inR2,1 strings are globally mapped to a torus (inR4). InR3,1 (and its conformal extensions) a prescription is given to obtain strings as integrals of real, bilinear spinor null vectors, from the Enneper-Weierstrass spinor representation of minimal surfaces, through the use of unitary transformations in spinor space which allows its restriction to the real (Majorana spinor-space). It is shown that the Nambu action, or the area of the world surface described by the space-time string, is minimized by the Lagrangian density expressed as a quadrilinear spinor product formally reminding Fermi and Thirring interaction Lagrangians.RiassuntoSi mostra come le vecchie espressioni integrali delle superfici minime in R3 di Enneper-Weierstrass e di quelle in R3,1 di Eisenhart se scritte con l’uso di polinomi quadratici spinoriali possono essere considerate come una particolare realizzazione della possibilità intravista da Cartan di considerare vettori ordinari come generati da piani isotropi in spazi complessi, nell’ambito della corrispondenza biunivoca di Cartan tra le direzioni di spinori puri e piani totalmente nulli in spazi complessi. Nel caso di R3 la realizzazione globale della corrispondenza di Cartan estende la parametrizzazione di Enneper-Weierstrass alla mappa conforme di Gauss della superficie minima su S2 che può essere identificata come la sfera celeste di Riemann. Per spinori reali, le superfici minime sono sostituite dacorde, sia in R2,1, che in R3,1; in R2,1, in particolare, la sfera di Gauss delle superfici minime è sostituita, nel caso delle corde, da un toro (in R4). In R3,1 (e le sue estensioni conformi) viene data una prescrizione per ottenere corde come integrali di vettori nulli reali, dalla rappresentazione spinoriale di Enneper-Weierstrass delle superfici minime, attraverso l’uso di trasformazioni unitarie nello spazio spinoriale, che permettono di ridurlo ad uno spazio reale (spazio degli spinori di Majorana). Si mostra come l’azione di Nambu, ovvero l’area della superficie spaziotemporale descritta da una corda dello spazio tempo, è resa minima da una « lagrangiana » avente la forma di un prodotto quadrilineare di spinori che formalmente ricorda il lagrangiano d’interazione di Fermi delle interazioni deboli e quello del modello di Thirring bidimensionale.
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: 
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- 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? 
 
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- 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? 
 
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- 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.
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.
125161041
Weyl Fields as a Basis for Unitary Symmetry
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.
118403927
Singular vector of W algebras via DS reduction of A2(1)
The BRST quantisation of the Drinfeld-Sokolov reduction applied to the case of A2(1) is explored to construct in an unified and systematic way the general singular vectors in W3 and W3(2) Verma modules. The construction relies on the use of proper quantum analoques of the classic DS gauge fixing transformations. Furthermore the stability groups W(gh) of the highest weights of the W Verma modules play an important role in the proof of the BRST equivalence of the Malikov-Feigin-Fuks singular vectors and the W algebra ones. The resulting singulary vectors are essentially classified by the affine Weyl group W modulo Wη. This is a detailed presentation of the results announced in a recent of theauthors.
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.