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Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1972"


Journal ArticleDOI
TL;DR: In this article, the results of the analytic evaluation of the electron form factors and of their zero-momentum transfer values, up to the fourth order of the perturbative expansion of QED in the electric charge, are presented.
Abstract: SummaryThe explicit results of the analytic evaluation of the discontinuities of the electron form factors and of their zero-momentum-transfer values, up to the fourth order of the perturbative expansion of QED in the electric charge, are presented. Asymptotic and threshold behaviours are discussed. The related form of the dispersion relations for the real parts is given.RiassuntoSi presentano i risultati espliciti del calcolo analitico delle discontinuità dei fattori di forma dell’elettrone e dei loro valori a momento trasferito nullo, sino al quart’ordine dello sviluppo perturbativo dell’elettrodinamica quantica nella carica elettrica. Si discutono i comportamenti asintotici e in soglia. Si dà la corrispondente forma delle relazioni di dispersione per le parti reali.РеэюмеПредлагаются точные реэультаты аналитического вычисления раэрывов злектронных форм-факторов и их эначений при нулевых передаваемых импульсах с точностью вплоть до четвертого порядка теории воэмушений по злектрическому эаряду в квантовой злектродинамике. Обсуждаются асимптотическое и пороговое поведения. Приводится соответствуюшая форма дисперсионного соотнощения для вешественных частей.

157 citations


Journal ArticleDOI
TL;DR: In this article, the symmetry properties of a particle interacting with an electromagnetic circularly polarized plane wave were considered and the classical and quantum analysis of the stability group of the plane wave exhibits the origin of the mass shift of the particle.
Abstract: We consider the symmetry properties of a particle interacting with an electromagnetic circularly polarized plane wave. The classical and quantum analysis of the stability group of the plane wave exhibits the origin of the mass shift of the particle. The Chakrabarti’s dynamical representation of the Poincare group is rederived and its physical meaning is given.

133 citations


Journal ArticleDOI
E. Barrelet1
TL;DR: In this article, an original method for the analysis of two-body reactions, based on the use of the zeros of the scattering amplitude, is presented. But this method is not suitable for the case of single body reactions.
Abstract: We present an original method for the analysis of two-body reactions, based on the use of the zeros of the scattering amplitude.

120 citations


Journal ArticleDOI
TL;DR: In this article, the results of the analytic evaluation of the discontinuities of the electron form factors and their zero-momentum transfer values, up to the fourth order of the perturbative expansion of QED in the electric charge, are presented.
Abstract: The explicit results of the analytic evaluation of the discontinuities of the electron form factors and of their zero-momentum-transfer values, up to the fourth order of the perturbative expansion of QED in the electric charge, are presented. Asymptotic and threshold behaviours are discussed. The related form of the dispersion relations for the real parts is given.

104 citations


Journal ArticleDOI
Edward Corrigan, David I. Olive1
TL;DR: In this article, the general dual vertex describing the transition of a Ramond fermion into a Neveu-Schwarz meson by the emission of general excited fermions was constructed.
Abstract: We construct the general dual vertex describing the transition of a Ramond fermion into a Neveu-Schwarz meson by the emission of a general excited fermion state. Our vertex thus generalizes the previous results of Thorn and Schwarz and is now put into a relatively compact and manageable form which enables us to check that certain of the general gauge conditions are correctly converted between the meson and fermion legs by the vertex. The particular construction of the vertex can be applied to the other older dual theories and leads to some new insights into them.

76 citations


Journal ArticleDOI
TL;DR: In this paper, the conformal covariance of the operator product expansion in the Thirring model is verified, but the vacuum state is invariant only under the O2,2 subalgebra of the infinite conformal algebra.
Abstract: The-infinitesimal generators of the infinite-dimensional conformal algebra in two space-time dimensions are constructed from the stress tensor. The conformal covariance of the operator product expansion in the Thirring model is verified, but the vacuum state is found to be invariant only under theO2,2 subalgebra of the infinite conformal algebra.

59 citations


Journal ArticleDOI
TL;DR: Gribov's derivation of the Glauber series and optical model from Feynman diagrams was generalized to nonzero scattering angles and any one-particle nuclear density as mentioned in this paper.
Abstract: Gribov’s derivation of the Glauber series and optical model from Feynman diagrams is generalized to nonzero scattering angles and any one-particle nuclear density

58 citations


Journal ArticleDOI
TL;DR: The anomalous magnetic momenta of the CERN muon storage ring was measured in this paper, and the result was (116 616±31)·10−8 compared with the theoretical value (116 588±2)· 10−8 showing agreement to (240±270) parts per million.
Abstract: The anomalous magnetic momenta≡1/2 (g−2) of the muon has been measured in the CERN muon storage ring. The result is (116 616±31)·10−8 compared with the theoretical value (116 588±2)·10−8 showing agreement to (240±270) parts per million. The lifetime of muons moving in a circular orbit with γ=12 was found to agree with the time dilation predicted by special relativity to within 1.1%. Details are given of the storage ring magnet, the instrumentation and the data analysis. The theoretical implications of the result are discussed.

50 citations


Journal ArticleDOI
TL;DR: In this article, the properties of physical states in dual-resonance models under rotations in the little group of the resonance momentum are studied, and it is shown how at a critical number of space-time dimensions this group can be represented just on the space of transverse states constructed by del Giudice, di Vecchia and Fubini (because these are then essentially the only states which couple).
Abstract: The properties of physical states in dual-resonance models under rotations in the little group of the resonance momentum are studied. It is shown how at a critical number of space-time dimensions this group can be represented just on the space of « transverse » states constructed by del Giudice, di Vecchia and Fubini (because these are then essentially the only states which couple). Further, the action of rotations in this group on the « photon » operatorsA n i is used to produce, for any number of dimensions, enough operators to create all the physical statesboth in the conventional model and in the model of Neveu and Schwarz.

46 citations


Journal ArticleDOI
TL;DR: In this article, the implications of crossing and analyticity properties on partial-wave amplitudes in the physical region were studied. And the results gave strong support to the model of Le Guillou, Morel and Navelet for ππs-waves.
Abstract: We study the implications of crossing and analyticity properties on partial-wave amplitudes in the physical region. We first show the physical interest of the ππ equations recently written by Roy; comparison with the Chew-Mandelstam equations is particularly instructive, and we show how these equations can be used:a) to construct low-energy amplitudes in practice, andb) to check the consistency of experimental data (adirect method for solving the «up-down» ambiguity and calculatings-wave scattering lengths is obtained). We then reconsider the Martin inequalities and the sum rules from which they are derived, and show that they can be used in a more powerful way. Our considerations and results give strong support to the model of Le Guillou, Morel and Navelet for ππs-waves. We finally give the general method for deriving physical-region crossing equations for arbitrary processes, in particular πN→πN.

43 citations


Journal ArticleDOI
TL;DR: In this article, the structure of parafermion algebras generated by N pairs of creation and annihilation operators is determined by the unique occurrence of certain representations of UN in particular representations ofSO2N and SO2N+1, identified by the eigenvalues of their invariants.
Abstract: It is pointed out that the structure of parafermion algebras generated byN pairs of creation and annihilation operators is determined by the unique occurrence of certain representations ofUN in particular representations ofSO2N andSO2N+1, identified by the eigenvalues of their invariants. This observation is used to derive a variety of identities satisfied by the creation and annihilation operators, which are characteristic of the orderp of the parastatistics. The «statistical quantum number» of Ohnuki and Kamefuchi is identified with the invariant ofSO2N and related in turn to the invariants ofUN. A simple method is stated for the systematic determination of special identities, some of which are already known.

Journal ArticleDOI
TL;DR: In this article, a substitute for phenomenological dispersion relations is proposed, which uses expansion of the scattering amplitude in terms of analytic functions to ensure the convergence and stability of the expansion.
Abstract: A substitute for phenomenological dispersion relations is proposed. The method uses expansion of the scattering amplitude in terms of analytic functions. The convergence and stability of the expansion are ensured by a prior probability measure on the expansion coefficients. The method is applied to the πN scattering amplitudes.

Journal ArticleDOI
TL;DR: Fermi's statistical model of high-energy hadron collisions is modified to take full account of resonance production, using the statistical bootstrap model of Hagedorn and Frautschi.
Abstract: Fermi's statistical model of high-energy hadron collisions is modified to take full account of resonance production, using the statistical bootstrap model of Hagedorn and Frautschi. Comparisons are made with experiments on\({\mathcal{N}}\overline {\mathcal{N}}\) annihilations at rest, the most favorable testing ground available. After adjustment of the single parameterR (the «interaction radius»), it is found that the multiplicity distributions and branching ratios are generally well fitted, except that events in which\({\mathcal{N}}\overline {\mathcal{N}}\) pairs are emitted occur less frequently than predicted, indicating that these channels are dynamically suppressed. The expected size of statistical fluctuations is discussed, as a basis for judging the results. The best fit is obtained withR=(1.6±0.25) fm, a little bigger than expected, but much more reasonable than the very large radii which were required in previous models. The maximum temperatureT0=(110±20) MeV corresponding to the fitted value ofR is lower than the figure usually quoted in fits to high-energy transverse-momentum distributions, but still matches reasonably well with these distributions when the full chain of secondary decays is properly included in the analysis. Some general features of resonance decay which follow from the model are discussed: in particular, the linear dependence of the multiplicity of decay products on the mass of the resonance.

Journal ArticleDOI
TL;DR: In this paper, a statistical generalization of the model is proposed, which allows one to separate the multi-paripheral and diffractive contributions to then-particle production cross-sections.
Abstract: The discussion of the multiperipheral bootstrap model in its one-dimensional version leads one to consider some experimental and theoretical inconsistencies, which are expected to be crucial at very high energies. A statistical generalization of the model is proposed; the new model allows one to separate the multiperipheral and diffractive contributions to then-particle production cross-sections. The general properties of the model are investigated.

Journal ArticleDOI
TL;DR: In this article, a rigorous derivation of the asymptotic properties of the one-loop nonplanar amplitude is given, which is controlled by the expected Regge singularities and possible exponentials.
Abstract: A rigorous derivation is given of the asymptotic properties of the one-loop nonplanar amplitude. Boths- andt-channel asymptotic behaviours are investigated. They are controlled by the expected Regge singularities and possible exponentials are ruled out. Thes-channel fixed-angle behaviour is again an exponential. The coefficient ofs in the exponential is exactly half of that obtained for the Born approximation and the planar loop.

Journal ArticleDOI
TL;DR: In this article, it is shown that the spontaneous violation of a gauge symmetry of the second kind results in the appearance not of Goldstone bosons but, rather, of massive gauge particles.
Abstract: It is known that the spontaneous violation of a gauge symmetry of the second kind results in the appearance not of Goldstone bosons but, rather, of massive gauge particles. The path-integral quantization of these theories is discussed here in general terms. The primary consideration is that quantities of physical significance, such as matrix elements of the scattering operator or the energy-momentum tensor, should be independent of the gauge in which the quantization rules are formulated. In particular, if it is possible to find one gauge in which the theory is unitary and another in which it is renormalizable, then the gauge-independent quantities must enjoy both these qualities. These ideas are applied to simple models with massive Yang-Mills fields and to a model which unifies the weak and electromagnetic interactions of electron-type leptons. Both these models appear to be unitary and renormalizable. The lepton theory is a relatively economical one. It involves five independent parameters: the electron charge and mass, the mass of the charged intermediate vector boson and the masses of a neutral scalar and a neutral vector boson.

Journal ArticleDOI
TL;DR: In this article, a few simple remarks on dilatation invariance in field theory and its relevance in connection with the short-distance behaviour of products of fields are made, and the relevance of these remarks is discussed.
Abstract: This note contains a few simple remarks on dilatation invariance in field theory and its relevance in connection with the short-distance behaviour of products of fields.

Journal ArticleDOI
TL;DR: In this article, the mean lives of low-lying levels in47Sc were measured using the Doppler-shift attenuation method with p-γ coincidences in the 44Ca(α, pγ)47Sc reaction.
Abstract: The mean lives of some low-lying levels in47Sc have been measured using the Doppler-shift attenuation method with p-γ coincidences in the44Ca(α, pγ)47Sc reaction. The following values have been obtained: >8 ps, (4.5±1.6) ps, (90±35) fs, >6 ps, (1.4±0.4) ps, (300±80) fs, (440±80) fs, <70 fs, (570±120) fs, (120±60) fs, (450±170) fs for the levels at 808, 1147, 1297, 1391, 1404, 1798, 1857, 1878, 2002, 2207, 2410 keV, respectively. Branchings of levels were also assigned. The present measurement allows us to propose a nearly complete level scheme for low-lying states in47Sc.M1 transitions are rather fast (of order of 0.1 W.u.) and alsoE1 transitions are not very hindered (of order of few 10−4 W.u.).

Journal ArticleDOI
TL;DR: In this article, a model of mesons as bound states of heavy quarks is considered, where low-lying mesons form linear trajectories with a slope of 1 (GeV)−2, and the modification of the vector-meson dominance form factor by the bound-state wave functions is calculated.
Abstract: The dynamics of strong binding of heavy scalar particles (quarks) are discussed with the help of the Bethe-Salpeter equation with a smooth ladder-type kernel. For this purpose, the Bethe-Salpeter amplitudes are expanded intoO4 spherical functions and the remaining « hyper-radial » equation is solved by a variational method. These calculations are considered as a model of mesons as bound states of heavy quarks. The low-lying mesons form linear trajectories with a slope of 1 (GeV)−2. The modification of the vector-meson dominance form factor by the bound-state wave functions is calculated and found to be in good agreement with experiment.

Journal ArticleDOI
C. Aragone1, Julian Chela-Flores1
TL;DR: In this paper, the content of the physical massive tensor field which enters in the 2-tensor theory formulated by Isham, Salam and Strathdee is studied.
Abstract: Making use of the small-excitation technique, we study the content of the physical massive tensor field which enters in the 2-tensor theory formulated by Isham, Salam and Strathdee. It is shown that the physical massive field contains, in general, a pure spin-2 field and one spin-0 field. By employing the ADM techniques, the sign of the energy for the free massive field is also analysed. Finally, we give the asymptotic behaviour for the spherically symmetric static free massive field. We also discuss the behaviour of this solution in the vicinity of the source.

Journal ArticleDOI
S. Frautschi1
TL;DR: In this article, the Fermi statistical model is modernized by including the full Hagedorn spectrum of resonances, and brought into correspondence with the Bohr model by assuming that the reaction proceeds via an incoherent sum over direct-channel resonances.
Abstract: Analogies between the statistical bootstrap model for hadrons and the familiar statistical model for nuclei are pointed out, and used as a guide for suggesting new statistical treatments of hadron reactions: i) the Fermi statistical model is modernized by including the full Hagedorn spectrum of resonances, and brought into correspondence with the Bohr model by assuming that the reaction proceeds via an incoherent sum over direct-channel resonances; ii) a definite prescription is given, predicting which hadron reactions should exhibit Ericson fluctuations; it is shown that the peaks and dips in\(\pi {\mathcal{N}}\) elastic scattering betweenp=1.5 and 5 GeV/c can be interpreted as Ericson fluctuations, although further experiments are needed to establish this interpretation definitively, iii) the rapidly falling cross-sections found in exotic exchange reactions such as backward K−p→K−p are interpreted as the incoherent part of the sum over a Hagedorn spectrum of direct-channel resonances; especially large Ericson fluctuations are predicted for such cases.

Journal ArticleDOI
TL;DR: In this paper, a one-dimensional theory of tachyons, which is non-invariant under space inversion and is based on extending the Lorentz transformations to inertial co-ordinate systems having relative velocities greater than that of light, is given.
Abstract: A one-dimensional theory of tachyons, which is noninvariant under space inversion and is based on extending the Lorentz transformations to inertial co-ordinate systems having relative velocities greater than that of light, is given. It is shown that the theory is fully causal and exhibits a reciprocity between tachyons and bradyons according to which a tachyon with velocity β>1 behaves as a bradyon with velocity 1/β<1 and with the space and time components of its «two-vectors» interchanged.

Journal ArticleDOI
TL;DR: In this article, the constraint equations imposed by the conservation of the electromagnetic current on the amplitudes describing the electromagnetic vertex, the π photoproduction, and the Compton effect on a target of arbitrary spin are formally solved.
Abstract: The constraint equations imposed by the conservation of the electromagnetic current on the amplitudes describing the electromagnetic vertex, the π photoproduction, and the Compton effect on a target of arbitrary spin are formally solved; the solution is manifestly Lorentz covariant and analytic, in the holomorphy, domain assumed for the amplitudes.

Journal ArticleDOI
TL;DR: In this paper, it is shown that the tree diagrams of the S-matrix are gauge invariant and that the Smatrix leads out of the physical subspace to a positive semi-definite metric.
Abstract: In the Yang-Mills theory a formalism corresponding to the conventional Gupta-Bleuler formalism in quantum electrodynamics leads to difficulties with regard to the probability interpretation. It is shown that the tree diagrams of theS-matrix are gauge invariant and that nevertheless theS-matrix leads out of the physical subspace Open image in new window with positive semi-definite metric. TheS-matrix projected onto the physical subspace hence is no longer unitary. In order to arrive at a unitary theory the original Gupta-Bleuler formalism has to be extended by introducing a complex scalar isovector field which obeys anticommutation rules. As a consequence, the usual connection between spin and statistics does not hold in the large state space. This does not pose any difficulty because an indefinite metric is used in the state space. The scalar fermions contribute in such a peculiar way as to cancel all bad effects of the Gupta-Bleuler ghosts in the original formulation, yielding, therefore, the correct Feynman diagrams with the usual analyticity properties. It is possible to give a consistent probability interpretation for the asymptotic particles within this formalism without any additional unitarization procedure. In comparison with quantum electrodynamics the ghost structure is much more complicated and the indefinite metric nontrivial. Nevertheless, our notation of good and bad ghosts with some modification remains the most suitable language also in this extended Gupta-Bleuler formalism.

Journal ArticleDOI
TL;DR: In this article, the authors present the results on total channel cross-sections obtained in the Saclay 180 l HBC exposed to a separated K− beam at Nimrod, at 13 incident K− momenta between 1.26 and 1.84 GeV/c.
Abstract: We present the results on total channel cross-sections obtained in the Saclay 180 l HBC exposed to a separated K− beam at Nimrod. The cross-sections for each channel are given at 13 incident K− momenta between 1.26 and 1.84 GeV/c.

Journal ArticleDOI
TL;DR: In this article, a new algebraic approach to the treatment of quantum problems is introduced, which allows us to understand completely the algebraic structure of all those systems whose eigenvalue equations can be reduced, by means of proper functional transformations, to the hypergeometric equation.
Abstract: A new algebraic approach to the treatment of quantum problems is introduced, which allows us to understand completely the algebraic structure of all those systems whose eigenvalue equations can be reduced, by means of proper functional transformations, to the hypergeometric equation. The results obtained constitute therefore the natural extension of the program we started in previous papers. In particular, it is proved that the eigenfunctions of the simple but physically interesting differential equation (3.8) are associated to the states of the irreducible representations Open image in new window (l=0,1,2,…) of the Lie algebraA1≈B1≈C1, characterized by the fact that the eigenvalue of the generatorJ3 of the algebra takes the constant value 1/2[1+2g]1/2 for the considered states. When consideration is given to theS-wave Schrodinger equation for two particles interacting through the Hulthen potential, it is proved that the energy levels are associated with a properly selected submanifold of the space carrying the irreducible representations Open image in new window or Open image in new window of the same algebra. Finally, a general procedure is introduced which allows an analogous treatment of all problems whose eigenvalue equations can be reduced to the hypergeometric equation. An interesting three-body problem is also exhaustively investigated from the algebraic point of view.

Journal ArticleDOI
TL;DR: In this article, various expansions to study the ground states of nuclei using Jastrow-type correlated wave functions are discussed, based on the Van Kampen decomposition method or developed as a power series in the parameter α of the two-nucleon correlation function f(r)=[1+αh(r)]1/2.
Abstract: Various expansions to study the ground states of nuclei using Jastrow-type correlated wave functions are discussed. The expansions are based on the Van Kampen decomposition method or are developed as a power series in the parameter α of the two-nucleon correlation functionf(r)=[1+αh(r)]1/2. Detailed numerical calculations have been performed on the ground state of4He by means of a central, soft-core nucleon-nucleon potential; the results are promising also from the point of view of a possible extension of the calculation to heavier nuclei.

Journal ArticleDOI
TL;DR: In this paper, the role of O4 expansion and the relation of scaling to small-distance behavior of interactions is made evident, and problems connected with gauge invariance are analysed.
Abstract: A concrete dynamical model is studied to obtain information on scaling and related problems. The role ofO4 expansion is pointed out, and the relation of scaling to small-distance behaviour of interactions is made evident. Problems connected with gauge invariance are analysed. The Schwinger-term sum rule forFL(ω) is discussed in the presence of Regge subtractions. The problem of analytic continuation of scaling functions into the annihilation channel is examined in a simple approximation.

Journal ArticleDOI
TL;DR: In this paper, the authors discuss problems associated with the extraction of compound nuclear lifetimes from blocking dips and compare different methods that may be used to quantify the filling-in of a blocking dip in a finite-lifetime case.
Abstract: In this paper we discuss problems associated with the extraction of compound nuclear lifetimes from blocking dips. This is done with reference to our previous measurements of the70Ge(p, p′)70Ge (1.04 MeV, 2+) and72Ge(p, p′)72Ge (0.835 MeV, 2+) reaction times. Different methods that may be used to quantify the filling-in of a blocking dip in a finite-lifetime case are discussed and compared. The importance of multiple-scattering effects in the various types of analyses are investigated. Our results are compared to those of other authors to obtain an estimate of the overall accuracy of the technique.

Journal ArticleDOI
A. Bassetto1, L. Sertorio, M. Toller1
TL;DR: In this paper, the authors examined the physical content and formal apparatus of multi-paripheralism and derived an exact factorized representation for the production amplitudes leading to a rigorous multi-peripheral integral equation.
Abstract: We examine the physical content and the formal apparatus of multiperipheralism, showing that their essence is an upper bound with suitable decrease and factorization properties. From this bound, we derive an exact factorized representation for the production amplitudes leading to a rigorous multiperipheral integral equation. We give the exact formulae for the total cross-section and then-particle inclusive distributions. The multiperipheral models studied so far appear as possible approximations of our equations.