123646189
On possible composite lepton states induced by neutrinos
SummaryStarting from the weak diagonal lepton Lagragian, a Bethe-Salpeter equation for the study of lepton bound states is set up. It is shown on general grounds that for aV−A current-current Lagrangian the free-lepton-bound-state vertex can only have the formΓ=γμ(1+γ5)Aμ. The kernel for a ladder approximation, corresponding to neutrino loop exchange, obeys a gauge condition and is only logarithmically divergent; it corresponds to ar−6 dependent force which is attractive for leptons-antileptons. A gauge-invariant technique of regularization of the kernel is given. The equations for the bound states have decoupled sectors. In particular, the equations for massless vector bound states having the quantum number of the photon are given. It is shown that in the Konopinski theory of leptons the muon would give a vertexΓ=γμ(1−γ5)Aμ and a model is presented by which a combination of electron-muon leptons could give rise to an effective electrodynamic Lagrangian for leptons. In such a model, lepton quantum electrodynamics would the finite; considering that in order to obtain massless vector composite states a regularization with masses of the order ofGF−1/2 is necessary, the standard local theory should keep its validity up to distances of the order ofGF1/2.RiassuntoPartendo dal Lagrangiano debole leptonico diagonale si costruisce un'equazione di Bethe-Salpeter per lo studio degli stati legati dei leptoni. Si mostra come in generale per un Lagrangiano del tipo·V−A corrente-corrente il vertice leptoni liberi-stato legato può avere solamente la formaΓ=γμ(1+γ5)Aμ. Il nucleo per una approssimazione a scala, corrispondente allo scambio di una bolla di neutrini, obbedisce ad una condizione di gauge ed è solo logaritmicamente divergente; esso corrisponde ad una forza dipendente della distanza comer−6, la quale è attrattiva per i leptoni-antileptoni. Si dà una tecnica di regolarizzazione del nucleo invariante di gauge. Le equazioni per gli stati legati hanno settori disaccoppiati. In particolare si danno le equazioni per stati legati vettoriali a massa nulla aventi i numeri quantici del fotone. Si mostra come nella teoria dei leptoni di Konopinski il muone produrrebbe un verticeΓ=γμ(1−γ5)Aμ e si presenta un modello per mezzo del quale una combinazione di leptoni elettronicimuonici potrebbe dar luogo ad un Lagrangiano elettrodinamico effettivo per i leptoni. In tale modello l'elettrodinamica quantistica dei leptoni sarebbe finita; considerando che è necessaria una regolarizzazione con masse dell'ordine diGF−1/2 per ottenere stati composti vettoriali a massa nulla, la teoria locale standard dovrebbe mantenere la sua validità fino a distanze dell'ordine diGF1/2.РезюмеИсходя из слабого диагонального лептонного Лагранжиана, выводится уравнение Бете-Салпетера для изучения лептонных связанных состояний. Из общих предположений показывается, что дляV−A ток-токового Лагранжиана вершина образования связанного состояния из свободных лептонов может иметь только видΓ=γμ(1+γ5)Aμ. Ядро для лестничного приближе\ соответствующего обмену нейтринной петлей, удовлетворяет условию калибровки и расходится только логарифмически. Это соответствует силе, зависящей какr−6, которая является силой притяжения для лептонов-антилептонов. Приводится калибровочно-инвариантный рецепт регуляризации ядра. Уравнения для связанных состояний имеют секторы, в которых связь отсутствует. В частности, приводятся уравнения для векторного связанного состояния с нулевой массой, которое имеет квантовое число фотона. Показывается, что в теории лептонов Конопинского мюон образовывал бы вершинуΓ=γμ(1−γ5)Aμ и предлагается модель, с помощью которой комбинация электронмюонных лептонов может привести к образованию эффективного электродинамического Лагранжиана для лептонов. В такой модели квантовая электродинамика лептонов была бы конечной. Учитывая, что, для того чтобы получить векторные составные состояния с нулевой массой, необходима регуляризация масс, порядкаGF−1/2, то стандартная локальная теория остается справедливой вплоть до расстояний порядкаGF1/2.
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.
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.
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.
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
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.