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In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an interesting multibeam generalization of the quantitative formulation of interferometric wave-particle duality, discovered by Englert for two-beam interferometers. The proposed generalization is an inequality that relates a generalized measure of the fringe visibility, to certain measures of the maximum amount of which-way knowledge that can be stored in a which-way detector. We construct an explicit example where, with three beams in a pure state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal which-way detector, that can achieve a better path-discrimination, at the same time as a better fringe visibility. In our opinion, this seems to be in contrast with the intuitive idea of complementarity, as it is implemented in the two-beams case, where an increase in path discrimination always implies a decrease of fringe visibility, if the beams and the detector are in pure states., Comment: 4 pages, 1 encapsulated figure. In press on Phys. Rev. A

We critically analyze the problem of formulating duality between fringe visibility and which-way information, in multibeam interference experiments. We show that the traditional notion of visibility is incompatible with any intuitive idea of complementarity, but for the two-beam case. We derive a number of new inequalities, not present in the two-beam case, one of them coinciding with a recently proposed multibeam generalization of the inequality found by Greenberger and YaSin. We show, by an explicit procedure of optimization in a three-beam case, that suggested generalizations of Englert's inequality, do not convey, differently from the two-beam case, the idea of complementarity, according to which an increase of visibility is at the cost of a loss in path information, and viceversa., Comment: 26 pages, 1 figure, substantial changes in the text, new material has been added in Section 3. Version to appear in J.Phys. A

Different criteria (Shannon's entropy, Bayes' average cost, Durr's normalized rms spread) have been introduced to measure the "which-way" information present in interference experiments where, due to non-orthogonality of the detector states, the path determination is incomplete. For each of these criteria, we determine the optimal measurement to be carried on the detectors, in order to read out the maximum which-way information. We show that, while in two-beam experiments, the optimal measurement is always provided by an observable involving the detector only, in multibeam experiments, with equally populated beams and two-state detectors, this is the case only for the Durr criterion, as the other two require the introduction of an ancillary quantum system, as part of the read-out apparatus., Comment: Latex, 16 Pages

By looking at fractional Dp-branes of type IIA on T_4/Z_2 as wrapped branes and by using boundary state techniques we construct the effective low-energy action for the fields generated by fractional branes, build their world-volume action and find the corresponding classical geometry. The explicit form of the classical background is consistent only outside an enhancon sphere of radius r_e, which encloses a naked singularity of repulson-type. The perturbative running of the gauge coupling constant, dictated by the NS-NS twisted field that keeps its one-loop expression at any distance, also fails at r_e., Comment: Latex file, 23 pages

We find a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers. Rather, they obey exotic commutation relations. These noncommutative properties drop out in the metric sector of the theory, where the Christoffel symbols and the Riemann tensor are ordinary commuting objects and they are given by the usual expression in terms of the metric tensor. Although the metric tensor is not a c-number, we argue that all measurements one can make in this theory are associated with c-numbers, and thus that the common invariant sector of our one--parameter family of deformed gauge theories (for the case of zero torsion) is physically equivalent to Einstein's general relativity., Comment: Latex file, 13 pages, no figures

Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group $ISO_q(3,1)$. Although the gauge fields, that is the spin--connection and the vierbeins are non--commuting objects depending on a deformation parameter, $q$, it is possible to construct out of them a metric theory which is insensitive to the deformation. The Christoffel symbols and the Riemann tensor are ordinary commuting objects. Hence it is argued that torsionless Einstein's General Relativity is the common invariant sector of a one--parameter family of deformed gauge theories., Comment: Latex file, 14 pages, no figures. Major changes in text. Contribution to the proceedings of the conference "Quantum Groups, Deformations and Contractions" Istanbul 1997, to be published in Turkish Journal of Physics. Title changed in journal to "The Quantum Poincare' Group as Hidden Symmetry of General Relativity"

A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the ordinary tetrad formalism with a q-deformed Poincare` group, the usual theory being recovered at q=1. Although written in terms of noncommuting vierbein and spin-connection fields, each theory has the same metric sector leading to the ordinary Einstein-Hilbert action and to the corresponding equations of motion. The Christoffel symbols and the components of the Riemann tensor are ordinary commuting numbers and have the usual form in terms of a metric tensor built as an appropriate bilinear in the vierbeins. Furthermore we exhibit a one-parameter family of Hamiltonian formalisms for general relativity, by showing that a canonical formalism a` la Ashtekar can be built for any value of q. The constraints are still polynomial, but the Poisson brackets are not skewsymmetric for q different from 1., Comment: LaTex file, 21 pages, no figures

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a q-deformed Poincare' gauge group symmetry, with the former recovered when q-> 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c-numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed., Comment: Latex file, 26 pages, no figures

We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field strengths become q-commuting fields. Our approach, which is explicitly carried out for the case of `minimal' deformations, has the advantage of leading naturally to a consistent Hamiltonian structure that has essentially all of the features of the undeformed case. For example, using the new Poisson brackets, the constraints form a closed algebra and generate q-deformed gauge transformations., Comment: 14 pages, latex, no figures. Two references added. In press on Phys. Lett. B

We describe a $n$ component abelian Hall fluid as a system of {\it composite bosons} moving in an average null field given by the external magnetic field and by the statistical flux tubes located at the position of the particles. The collective vacuum state, in which the bosons condense, is characterized by a Knizhnik-Zamolodchikov differential equation relative to a $\hat {U}(1)^n$ Wess-Zumino model. In the case of states belonging to Jain's sequences the Knizhnik-Zamolodchikov equation naturally leads to the presence of an $\hat{U}(1)\ot \hat{SU}(n)$ extended algebra. Only the $\hat{U}(1)$ mode is charged while the $\hat{SU}(n)$ modes are neutral, in agreement with recent results obtained in the study of the edge states., Comment: 11 pages, Latex

We show that a Coulomb gas Vertex Operator representation of 2D Conformal Field Theory gives a complete description of abelian Hall fluids: as an euclidean theory in two space dimensions leads to the construction of the ground state wave function for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a $1+1$ Minkowski theory gives the corresponding dynamics of the edge states. The difference between a generic Hall fluid and states of the Jain's sequences is emphasized and the presence, in the latter case, of of an $\hat {U}(1)\otimes \hat {SU}(n)$ extended algebra and the consequent propagation on the edges of a single charged mode and $n-1$ neutral modes is discussed., Comment: Latex, 22 pages

By using the explicit knowledge of the lowest energy single particle wave functions in the presence of an {\it arbitrary} magnetic field, we extend to the case of a torus Jain's idea of looking at the FQHE as a manifestation of an integer effect for {\it composite fermions}. We show that this can be realized thanks to a redefinition of the vacuum state that is explicitly collective in nature. We also discuss the relationship of this approach with the hierarchical scheme and with the characterization of the Hall states in terms of $W_{1+\infty}$ algebras and 2D conformal field theories., Comment: 12 pages, LATEX, DSF-T-94/17-INFN-NA-IV-94/17