119020204
Weyl and conformal covariant field theories
SummaryIt is shown that, by imposing covariance with respect to the 11-parameter Weyl group, most of the known renormalizable field theories, and only these, are obtained and that they admit, locally in the Minkowski spaceM3,1, a conformal group as a higher symmetry group. Globally conformal covariant Lagrangian field theories are first defined in a pseudo-Euclidean spaceM4,2, where the conformal group acts linearly. Subsequently, a compactified Minkowski spaceMc3,1 is defined where the ordinary Minkowski space is densely imbedded. Conformally invariant Lagrangians and corresponding quasi-invariant massive-field equations inM4,2,Mc3,1,M3,1 are considered and the transformation properties of the mass terms discussed. Conformal quasi-invariant field equations for spinor fields interacting with (conformal) scalar and vector fields are discussed. The spinor fields always appear in the equations of motion as doublets of Dirac spinors, both having canonical dimensions. The simplest form of minimally coupled spinor-vector field equations appears to be apt to represent intermediate boson weak interactions rather than electromagnetic ones, since the interaction always induces transitions among the elements of the spinor doublets. To obtain the familiar field equations of electrodynamics, one may introduce appropriate conformally covariant factors in the spinor-vector Lagrangian density. By imposing two conformally invariant gauge conditions on the conformal six-vector field, one obtains conformally covariant Dirac-Maxwell field equations inM3,1 for a conformal doublet of equally charged fermions (reminiscent of μ, e). By not imposing any gauge condition on the conformal vector field, two new Lorentz scalar fields,A+,A−, coupled to the spinor doublet, are predicted by the conformal theory. Their properties and possible role in mass generation are briefly discussed.RiassuntoSi fa vedere come, imponendo la covarianza rispetto al gruppo di Weyl ad 11 parametri, si ottiene la maggior parte delle teorie di campo rinormalizzabili conosciute e solamente queste, e come esse ammettano, localmente nello spazio di MinkowskiM3.1-un gruppo conforme come gruppo di simmetria più elevata. Teorie di campo lagrangiane globalmente conformi covarianti vengono definite dapprima in uno spazio pseudo, euclideoM4.2, dove il gruppo conforme agisce linearmente. Si definisce quindi uno spazio di Minkowski compattificatoMc3,1, dove lo spazio di Minkowski usuale è immerso densamente. Si considerano inM4.2,Mc3,1,M3,1 lagrangiani conformi invarianti e le equazioni di campo massive quasi invarianti corrispondenti, e si discutono le proprietà di trasformazione dei termini di massa. Si discutono le equazioni di campo conformi quasi invarianti per campi spinoriali interagenti con campi scalari e vettoriali (conformi). I campi spinoriali appaiono nelle equazioni del moto sempre come doppietti di spinori di Dirac, entrambi aventi dimensioni canoniche. La forma più semplice di equazioni di campo per spinori e vettori, con minimo accoppiamento sembra essere più adatta a rappresentare le interazioni deboli con bosoni intermedi, piuttosto che quelle elettromagnetiche, in quanto l’interazione induce sempre transizioni fra gli elementi del doppietto di spinori. Per ottenere le usuali equazioni di campo dell’elettrodinamica, si possono introdurre appropriati fattori conformi covarianti nella densità di lagrangiano spinore-vettore. Imponendo due condizioni di gauge conformi invarianti sul campo esavettoriale conforme, si ottengono inM3,1 equazioni di campo di Dirac-Maxwell conformi covarianti per un doppietto conforme di fermioni con carica eguale (che potrebbero rappresentare μ, e). Non imponendo alcuna condizione di gauge sul campo vettoriale conforme, la teoria conforme predice due nuovi campi, scalari di Lorentz,A+,A−, accoppiati al doppietto di spinori. Si discutono brevemente le loro proprietà ed il ruolo possibile nella generazione di massa.РезюмеПоказывается, что, накладывая условие ковариантности относительно 11-параметрической группы Вейля, получается большинство известных перенормируемых теорий поля. Эти теории допускают локально в пространстве МинковскогоM3,1 конформную группу, как группу более высокой симметрии. Сначала определяются глобально конформные ковариантные Лагранжианные теории поля в псевдо-эвклидовом пространствеM4,2, где конформная группа действует линейно. Затем определяется компактное пространство МинковскогоMc3,1 в которое вставлено обычное пространство Минковского. Рассматриваются конформно инвариантные Лагранжианы и соответствующие квази-инвариантные уравнения для массивных полей вM4,2,Mc3,1,M3,1. Обсуждаются свойства преобразований массовых членов. Анализируются конформные квази-инвариантные уравнения поля для спинорных полей, взаимодействующих с (конформными) скалярным и векторным полями. Спинорные поля всегда возникают в уравнениях движения, как дублеты спиноров Дирака, причем оба поля имеют канонические размерности. Простейшая форма уравнений, минимально связанных спинорно-векторных полей, по-видимому, представляет промежуточный бозон слабых взаимодействий, а не электромагнитных, так как взаимодействие всегда индуцирует переходы между элементами спинорных дублетов. Для получения аналогичных уравнений поля для электродинамики можно ввести в плотность спинорно-векторного Лагранжиана соответствующие конформно ковариантные факторы. Накладывая на конформное шести-векторное поле два конформно инвариантных условия калибровки, мы получаем конформно ковариантные уравнения поля Дирака-Максвелла вM3,1 для конформного дублета одинаково заряженных фермионов (напоминающих м, е). Не накладывая никаких условий калибровки на конформное векторное поле, конформная теория предсказывает два новых скалярных поля Лоренца,A+,A−, связанных со спинорным дублетом. Обсуждаются свойства этих полей и их роль в образовании масс.
125161041
Weyl Fields as a Basis for Unitary Symmetry
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.
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.
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.