Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1976"

Conformal Invariance in Quantum Mechanics

Abstract: The properties of a field theory in one over-all time dimension, invariant under the full conformal group, are studied in detail. A compact operator, which is not the Hamiltonian, is diagonalized and used to solve the problem of motion, providing a discrete spectrum and normalizable eigenstates. The role of the physical parameters present in the model is discussed, mainly in connection with a semi-classical approximation.

The classical mechanics for bose-fermi systems

Abstract: In this paper we study in a systematic way the classical mechanics of systems described byc-number variables and by Grassmann variables. We derive the general form of the nonrelativistic action and we study the theory of canonical transformations. For a general action, we show that the Jacobian matrices of the canonical transformations acting onN Grassmann variables form a groupO N, N . This group becomesO N for the nonrelativistic action, due to the presence of second-class constraints. We study some examples which give rise to a correct classical description of the spin. Considering a relativistic extension of one of these models, we get a first quantized «substratum» for the superfield theories.

On the quantization of systems with anticommuting variables

Abstract: In this paper we consider the pseudomechanics, that is the mechanics of a system described by ordinary canonical variables and by Grassmann variables. We study the canonical formalism and in particular we define the Poisson brackets. We show that the algebra of the Poisson brackets is a graded Lie algebra. Using this fact as a hint for quantization we show that the corresponding quantized theory is the ordinary quantum theory with Fermi operators. It follows that the classical limit (ħ → 0) of the quantum theory is, in general, the pseudomechanics.

Supersymmetries and the pseudoclassical relativistic electron

Abstract: In this work we consider a version of the supersymmetry parametrized by anticommuting pseudovector and pseudoscalar variables instead of spinorial ones. We construct a pseudoclassical relativistic Lagrangian invariant under the former supersymmetry. This Lagrangian is a degenerate one and we show that, after quantization, one of the constraints gives rise to the Dirac equation. Moreover, we introduce into our Lagrangian an interaction term with an external electromagnetic field, and we show that this is possible, in a consistent way, only if the anomalous magnetic moment is vanishing. It follows that this model represents a pseudoclassical description for the relativistic electron.

A new approach to conformal invariant field theories

Abstract: A new approach to conformal invariant field theories is presented. The physical idea is to introduce a fundamental scale of hadron phenomena by means of a dilatation noninvariant vacuum state in the framework of a scale-invariant Lagrangian field theory. A new unconventional feature is that this programme can only be carried out if the «vacuum» state is not translation invariant. The «vacuum» is still invariant under a 10-parameter subgroup of the full conformal group but this subgroup does not coincide with the Poincare group. A physical interpretation based on an appropriate averaging on an infinite ensemble of equivalent «vacuum» states allows to preserve energy momentum conservation, which is defined within a thermodynamical framework.

On a class of Lagrangian models for massive and massless Yang-mills fields

Abstract: We discuss renormalization for a class of Lagrangians containing an explicit mass term for the vector field and a four-vertex for the Faddeev-Popov ghost field. The action is shown to be invariant under nonlinear gauge transformations, which are a generalization of those introduced by Becchi, Rouet and Stora. This invariance guarantees the validity of the Slavnov-Taylor identities, which are then used to discuss the renormalization of the theory. The problem of unitarity is not discussed here. Canonical and Lorentz-covariant formalism is employed.

Mean charged hadron multiplicities in high-energy collisions

Abstract: A collection of mean charged hadron multiplicities per inelastic collisions in various high-energy processes is presented. An extensive list of fits of 〈n ch〉 as a function of energy is presented and discussed. As the energy increases the multiplicities for different collisions tend to a unique curve, independent of the types of colliding particles.

An alternative approach to the proof of unitarity for gauge theories

Abstract: The proof of unitarity for gauge theories involving a Faddeev-Popov ghost is revisited. We assume the existence of a generatorF of the Slavnov transformations. The subspace of the unphysical one-particle states is that spanned byF. Under the assumption thatF is conserved and obeys the conditionF2=0, we prove that the unphysical states do not contribute to the unitarity equation restricted to the physical subspace.

The unitarity problem and the zero-mass limit for a model of massive yang-mills theory

Abstract: In a previous paper we proposed a Lagrangian model for a massive Yang-Mills field. This model exhibits invariance under the Slavnov transformations proposed by Becchi, Rouet and Stora. This invariance implies the Slavnov-Taylor identities. Here we study the problem of unitarity and gauge invariance. For a massless field one can prove physical unitarity and gauge invariance at the formal level,i.e. by ignoring infra-red problems. Form≠0 theS-matrix is not unitary and gauge invariant, when restricted to the physical subspace. We show how these properties are restored in the limit of zero mass.

Higgs model and supersymmetry

Abstract: The Higgs model can be made supersymmetric, provided a Dirac spinor is added, and the quartic interaction term in the Lagrangian density is —(e2/2)(ϕ†φ)2, wheree is the gauge coupling constant. The model describes a vector, a Dirac spinor and a real scalar; it depends only on two arbitrary parameters,m ande. As a gauge-invariant model, it can be studied in a Wess-Zumino gauge, or in a supersymmetric gauge. It can also be obtained as a theory of a self-interacting vector multiplet. Finally, it is suggested that a scalar particle may be associated with the photon and the two neutrinos in the theory of weak and electromagnetic interactions.

Vacuum polarization and photon propagation in a magnetic field

Abstract: The vacuum polarization tensor in the presence of a static homogeneous magnetic field is calculated exactly as a function of both the magnetic field and the wave vector, and is regularized explicitly by using Shabad’s diagonalization with respect to tensor indices The wave properties for the two electromagnetic modes in the birefringent vacuum are calculated exactly using a technique from plasma physics The strongfield limit is considered explicitly and it is shown that the two modes reduce to forms equivalent to the magnetoacoustic and shear Alfven modes in a plasma with Alfven speed much greater than the speed of light

About new space-time symmetries in relativity and quantum mechanics

Abstract: Some consequences of the space-time symmetries previously studied within extended relativity are exploited, and that study is improved. In particular, it is shown that relativity requires antiparticles to be formally associated withnegative rest masses (but withpositive relativistic masses and energies, of course!). The physical and geometrical meaning ofchirality P5 is derived, in such a context, and shown to be essentially connected with the inversion of afifth axis (axis related to the rest-mass). Infive dimensions, from the frame with all the (five) axes inverted, an observer woulde.g. describeantimatter exactly so as the initial (noninverted) observer would describematter, andvice versa. By applying what precedes to relativistic quantum mechanics (e.g. to fermion fields and Dirac equations), we get—among other things—a «strong\(\bar C\bar P\bar T\) theorem » (see the text): « Under inversion of all five axesx, y, z, t, m0, not only physical laws (of mechanics and electromagnetism, at least) are covariant, but even physical fields are invariant ».

On Delbrück scattering

Abstract: The formulae for the amplitudes of Delbruck scattering given in a previous paper are manipulated and much simpler expressions for them are derived having the form of a sum of twofold and threefold integrals. The integrands are rather compact and contain only rational, irrational and logarithmic functions. In this preliminary work we consider only the amplitudea+− for circularly polarized photons and we give numerical results for photon energy equal to 10.83 MeV and scattering angle in the range from 50° to 150°. For what concerns the real part of the amplitudes, these preliminary results allow one to resolve the discrepancy between the numerical results previously obtained by Ehlotzky and Sheppey and those more recently given by Papatzacos. In fact our results agree with those by Papatzacos and this seems to confirm that the fixed-angle dispersion relation used by Ehlotzky and Sheppey for the calculation of the real parts is incorrect.

Dimensional Regularization and Anomalies

Abstract: The renormalized Callan-Symanzik equation and chiral Ward identity for QED are derived in the framework of dimensional regularization. A new proof of the Adler-Bardeen theorem on the absence of radiative corrections in the triangle anomaly is obtained.

Muon transfer to heavy atoms: A probe for the study of the (μp)2S system

Abstract: The transfer process of a negative muon from the (μp)1S-and the (μp)2S-state to a heavy atom (Z≳10) is studied by using a semi-classical approximation; the electron shielding and the (μp) tunnelling through the atomic potential are considered Estimates of the transfer cross-section are given It is found that the transfer from the 2S-state is faster than from the 1S-state by a factorλ2S/λ1S ⋍ 90Z−1/2 It is suggested, therefore, that the transfer process can be an useful probe to study the (μp)2S atom

Thermal excitation of nucleons in relativistic high-density nuclear shock waves

Abstract: The possibility of excitation of nucleonic resonances in relativistic heavy-ion collisions is investigated. The high-density nuclear shock waves are treated in a relativistic hydrodynamical model.

M1 strength distribution in nuclei

Abstract: TheM1-transitions in nuclei are studied by means of sum rules. A useful sum rule for the total strength of theM1-excitations is given in terms of the number of the nucleons which are in the nonfilledl-shell. The well-known Kurath sum rule for the energy-weighted total strength is generalized to include the two-body potential contribution. The centroid of the excitation is studied; finally the isotopic spreading of theT upper andT lower component of the excitation is analysed and the «symmetry energy» for theM1-transitions is studied. Not only the centroid shift, but also the isotopic splitting is an effect due toSU4-breaking terms of the nuclear Hamiltonian, in particular the spinorbit, Bartlett, Heisenberg terms.

Elastic scattering of π±-mesons on4He in the energy interval (68÷208) MeV@@@Рассеяние эаряженных пионов на ядрах4He в диапаэоне знергий (68÷208) MзB

Abstract: SummaryDifferential cross-section measurements of elastic scattering of π± on4He are presented. The experiment was carried out with the high-pressure helium self-shunted streamer chamber surrounded by a hodoscope of scintillation counters. Measurements were fulfilled both for positive and negative pions at 68, 98, 135, 145 and 156 MeV, for negative pions also at 120, 174 and 208 MeV. The differential and total elastic-scattering cross-sections are compared with optical-model calculations using the Kisslinger and Laplacian potentials. Some results, obtained from an energy-dependent phase shift analysis, are also presented.RiassuntoSono presentati i risultati della misura della sezione d’urto differenziale di diffusione elastica (π±,4He) a 68, 98, 135, 145, 156 MeV e (π−,4He) a 120, 174, 208 MeV. I dati sperimentali sono confrontati con le previsioni del modello ottico. È stata pure fatta un’analisi in fase dipendente dell’energia.РеэюмеПриводятся новые данные по дифференциальным сечениям упругого рассеяния эаряженных пионов на ядрах гелия-4, полученные в зкспериментах с гелиевой стримерной камерой высокого давления на синхроциклотроне ЛЯП ОИЯИ. Приводятся данные по фаэовому аналиэу, эависяшему от знергии, проводится сравнение с расчетами по оптической модели.

Measurement of Two-Particle Semi-Inclusive Rapidity Distributions at the CERN ISR.

Abstract: We present data on the semi-inclusive distributions of rapidities of secondary particles produced in pp collisions at very high energies. Our experiment was performed at the CERN Intersecting Storage Rings (ISR). The data given here, at centre-of-mass energies of √s=23 and 62 GeV, include the single-particle distributions and two-particle correlations. The semi-inclusive correlations show pronounced short-range correlation effects which have a width considerably narrower than in the case of inclusive correlations. We show that these short-range effects can be understood empirically in terms of three parameters whose energy and multiplicity dependence are studied. The data support the picture of multiparticle production in which clusters of small multiplicity and small dispersion are emitted with subsequent decay into hadrons.

High-spin states in48Ti and46Ti

Abstract: Strong γ-ray yrast cascades were observed in46,48Ti with the reactions44Ca(7Li, p2n)48Ti,27Al(24Mg, 3p)48Ti,48Ca(3He, 3n)48Ti and40Ca(12C, α2p)46Ti. In-beam γ-ray excitation functions, γ-ray angular distributions and γ-γ coincidences were performed. The following new levels were observed (Ex in keV):48Ti: 3510.0, 62+, 4565.9, 8+, 6104.7, 10+ and 6737.4 (11+, 12+);46Ti: 4643.5, (8+), 6242.0, (10+), 6514.0 (11+, 12+). All these new levels as well as the known yrast states in even-even 1f7/2 nuclei are well understood in the frame of the extreme 1f7/2)n shell model particularly the very-high-spin states.

Elastic scattering of π±-Mesons on3He in the energy interval (68÷208) MeV

Abstract: Different cross-section measurements of elastic scattering of π± on3He are presented. The study was done both for positive and negative pions at 98, 120, 135, 145, 156 MeV, for negative pions also at 198 and 208 MeV and for positive pions also at 68MeV. The experiment was carried out with a high-pressure helium self-shunted streamer chamber surrounded by a hodoscope of scintillation counters. The results are compared with optical-model calculations using spin-and isospin-dependent potentials. The energy dependence of the total elastic (π±,3He) scattering cross-section is discussed. Estimates of the (π3He3H) coupling constant according to the theory of Chew and Low are presented.

A set of wave equations for massless fields which generalize weyl and maxwell equations

Abstract: The Weyl and Maxwell equations are shown to have generalizations for massless fields of any helicityλ. The set of equations obtained in this way does not belong to already classified sets. One of the most interesting features is that the Dirac γμ-matrices are generalized. The generalizedγ0-matrix has the three following properties: i) it is a parity operator, ii) it occurs in the definition of a Lorentz-invariant scalar product like \(\bar \psi \)=ψ+γ0ψ, iii) it is the time component of a completely symmetric tensor of order 2λ.

Proton stripping and pion production in relativistic deuteron-nucleus collisions

Abstract: We construct a Glauber theory for the proton stripping and the pion production in relativistic deuteron-nucleus collisions, taking into account the relativistic dilation of the internal deuteron wave function. The theory is applied to the experiments performed at the Bevalac with 1.05 and 2.1 GeV/nucl. incident deuterons. The observed broadening of the stripped proton spectrum is explained as coming from the relativistic dilation effect. The production of fast pions is described as initiated from nucleons of the incident deuteron, whose momenta are large, again due to the relativistic dilation. Both the momentum shapes and theΛ-dependence of the cross-sections for the different reactions are well reproduced.

Analysis of γn→nπ+π- and γn→pπ-π0 reactions from threshold up to 1 GeV

Abstract: The final results of a bubble chamber experiment on double pion photoproduction in deuterium, from threshold up to 1 GeV, are reported. The total cross-sections of reactions γn→nπ−π+, γn→pπ−π0 and γp→pπ+π− are calculated, by using the spectator model. The squared-mass distributions have been fitted, and the cross-sections of reactions γn→Δ−π+, γn→Δ+π−→pπ0π− and γp→Δ++π− have been obtained. The general features of these cross-sections are consistent with a large nonresonant Δ production, accounted for in a gauge-invariant OPE model.

Clusters and the rapidity interval method

Abstract: An effective method of analysing the experimental jets with the aim of discovering the clusterization phenomenon of particles produced in high-energy inelastic processes is proposed. The method exploits the set of all possible rapidity intervals,i.e. rapidity differences of two particlesyi+k+1 −yi with somek particles having rapidities in between (the usual gap corresponds tok = 0). It provides information which is in principle as complete as that obtained from the correlation functions. It is simple in application and physically clear. The method is applied to various models and the rapidity interval distributions thus obtained are compared to the experimental data for π−p 40 GeV and pp 70 and 200 GeV collisions. The important role of clusterization of secondary particles follows from this comparison. It is predicted that the two-bump structure should develop fork ≥ 4 and large multiplicities in pp interactions at 200 GeV if two baryonic clusters were produced.

A strong-coupling approximation: Covariant perturbation expansion around independent-valued field theories

Abstract: A covariant perturbation expansion is developed around Klauder’s independent-valued field theories as zeroth approximation. A diagram technique is constructed and an analytic regularization is introduced to handle the superficially divergent terms of the expansion. For a wide class of interactions, the divergent terms can be either compensated by renormalization or vanish identically after the removal of the regularization. As a result only tree diagrams are found to contribute to the various Green’s functions; nonetheless one finds nontrivial scattering amplitudes with correct clustering and positivity properties.

How to Recover Causality for Tachyons Even in Macrophysics.

Abstract: The postulate that negative-energy particles do not exist (travelling forward in time) leads automatically to the « Reinterpretation Principle » by Stuckelberg and by Feynman. It has been already shown that such a « principle », assumed as theThird postulate of special relativity, ensures the validity of the law of (retarded) causalityboth in standard relativityand in (extended) relativity with tachyons and with Superluminal inertial frames. OurThird postulate, moreover, allows predicting antiparticle existence in apurely relativistic context. In this paper we show that theThird postulate is enough to implement the law of causality even in macrophysics, when usual macro-objects interact with microtachyons and macrotachyons. To that aim, some tachyon kinematics is further developed, which can be useful even in understanding elementaryparticle interactions (andmay be hadron structure). Many other related problems are discussed.

Experimental values for the static nuclear polarizability

Abstract: The recent experimental determination of total photonuclear cross-sections σγT allows a model-independent calculation of static nuclear polarizabilities. The experimental values of this second-order nuclear-structure constant are compared to Migdal’s prediction of the static nuclear polarizability. This prediction is based on the assumption that the asymmetry energy taken from Weizsacker’s mass formula is the essential parameter entering the expression for the restoring force in response to an external electric field. The experimental values of the nuclear polarizability for all elements investigated (A⩽40) were found to be roughly three times larger than Migdal’s polarizabilities and about two times larger than the values deduced from the partial cross-sections σγn even for the high-Z elements for which σγn should be very nearly equal to σγT .

Algebraic approach to the quark problem

Abstract: An algebraic framework is constructed for the description of color singlet states composed of colored quarks. Quark fields are elements of a local octonionic module. Invariant actions are constructed for the quark fields. The actions are symmetric under local color transformations belonging to the exceptional Lie groupG2. The theory is quantized in a generalized path integral formalism. It is found that only color singlet states propagate, whereas quarks are «confined».

Sum rule approach to radiative pion capture in nuclei

Abstract: The radiative pion capture in nuclei has been studied by sum rules techniques. Two simple sum rules for the radiative-capture rates from 1s and 2p orbits are given in terms of the mean photon momentum, the nuclear density and the wave function of the pion. Explicit calculations are performed for4He,6Li,10B,12C,14N,16O where experimental results are available.