Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1979"

Gauge theories and strong gravity

Abstract: We discuss in detail the classical solutions of two field theoretical models invariant under general variable transformations. In particular we examine the case of a Yang-Mills theory and of a four-dimensional nonlinear sigma model, both coupled to “strong gravitation». Instanton, meron and multimeron configurations are obtained and their properties discussed.

θ-vacua in two-dimensional quantum chromodynamics

Abstract: It is shown that θ-vacua exist in two-dimensional non-Abelian gauge theories, as well as in the Abelian theories.

Interference, gravity and gauge fields

Abstract: The phase shift due to gravitational field and all gauge fields in the interference of two coherent beams is obtained. In the case of gravitation, it is shown, for a particle with arbitrary spin, that there exists a phase shift due to the coupling of spin to space-time curvature. This and the corresponding phase shift for gauge fields are analogous to the Aharonov-Bohm effect. The classical limit for particles moving in gravitational and gauge fields is obtained from the phase shift. For gravitation, in the absence of torsion, this is the Mathisson-Papapetrou equation, which is thereby shown to be the classical limit of the Dirac and Bargmann-Wigner wave equations, generalized to curved space-time. In the presence of torsion, a modification of this equation, given by Hehl, is obtained. It is pointed out that gravity is not a pure gauge field and that it must be placed in the more general category of an «interference field» which contains both gravity and gauge fields as special cases. The field equations for gauge fields and gravity are obtained from the heuristic assumption that a particle acts on a field in a manner which depends on how it responds to the field via the phase shift. For gauge fields, they contain the Yang-Mills equations as a special case. For gravity, a modification of Einstein’s field equations is obtained, which corresponds to the Lagrangian (1/16πK) ·, · (2Λ +R) + (1/32πf)RμνϱσRμνσϱ, where the Riemann tensor contains torsion andK, f, Λ are constants (Λ may be zero). The relevance of the phase shift, due to rotation, to the quantization of vortices in superfluid helium is pointed out. This suggests that the curl of the superfluid velocity may obey a system of equations analogous to Maxwell’s equations and the analogue of the magnetic monopole for superfluid helium is also introduced.

Small-time behaviour of quantum nondecay probability and Zeno's paradox in quantum mechanics

Abstract: A detailed investigation of the small-time deviations of the quantum nondecay probability from a pure exponential is made to study their physical consequences. Specific consideration is given to the problem of the dependence of the lifetime on the characteristics of the measuring apparata whose possible occurrence has recently been pointed out. In particular we investigate the problem of the indefinite increase of the lifetime when the frequency of the measurement processes tends to infinity, an effect referred to as Zeno's paradox in quantum mechanics. It is shown that, if the uncertainty relations are properly taken into account, the arguments leading to the paradox are not valid. Moreover, by the same kind of arguments, it is shown that the dependence of the measured lifetime on the frequency of the measurement processes, even though present in principle, is practically not detectable. To verify experimentally that the reduction process is effective one must then resort to the comparison of an experiment with reductions with one in which no interactions with the environment take place.

On the Aharonov-Bohm effect

Abstract: The recent claim by Bocchieri and Loinger that the Aharonov-Bohm effect has a purely mathematical origin is critically examined. We analyse their arguments in detail and show that they are based on an invalid use of gauge-dependent and representation-dependent effects which renders their conclusion incorrect. We also briefly discuss the more recent experiments that confirm the existence of the Aharonov-Bohm effect.

On unitary quantum mechanics

Abstract: The paper proposes a model of a unitary quantum field theory where the particle is represented as a wave packet. The frequency dispersion equation is chosen so that the packet periodically appears and disappears without changing its form. The envelope of the process is identified with a conventional wave function. Equations of such a field are nonlinear and relativistically invariant. With proper adjustments they reduce to Dirac, Schrodinger and Hamilton-Jacobi equations. A number of new experimental effects is predicted both for high and low energies.

Inclusive spectra of pions produced in high-energy interactions

Abstract: Accelerator data on the inclusive spectra of secondary pions produced in high-energy hadron-hadron collisions are critically analysed. A range of secondary-particle spectra is derived from kinematical considerations, by taking into account the experimentally observed dependence of the total multiplicity of the secondaries on the primary-particle denergy. Two extreme cases are obtained if either Feynman’s scaling or a pure statistical model is taken. Parametrization of the variation with primary energy of the spectrum of secondaries in the central region seems also to describe spectra in the fragmentation region. The formula which gives the best fit to the data over the whole FNAL and ISR range differs from that predicted for Feynman scaling at least as much as from that obtained on the basis of the statistical-type approach.

The gauge technique

Abstract: The gauge technique is a procedure whereby the Ward identities of a gauge theory are exatly solved to provide the longitudinal components of the Green's functions as functionals of the pure charged-line amplitudes. In quantum electrodinamics, for instance, the two-electron multiphoton amplitudes are determined by the electron propagator, which can itself be found via the Dyson-Schwinger equations: thus the procedure is gauge covariant and self-consistent. In this manner one readily obtains the infra-red properties of the amplitudes both for relativistic and nonrelativistic (axial) gauge-fixing schemes. The transverse components of the amplitudes are generated iteratively via the skeleton expansion using the gauge-covariant vertices and propagators determined by the gauge technique. As the method is nonperturbative, the prospect of applying it to the infra-red behaviour in chromodynamics looks promising.

Time symmetry and the einstein paradox. ii

Abstract: The characteristic difference between the paleoquantal calculation (addition of partial probabilities) and the neoquantal one (addition of partial amplitudes) for the correlation of photon polarizations in cascade transitions is derived in terms of elementary trigonometry. This deliberate use of simple formulae aims at a transparent rendering of the change in paradigm required by the so-called EPR paradox (which is truly the 1927 Einstein paradox), namely that 1) the two photons donot possess polarizations of their own when leaving the source C, butborrow onelater, when interacting with the analysersL andN; 2) the die is thus not cast atC, but later, atL andN; 3) the correlation between the measurements atL andN is tied throughC, in their common past. The tight connection between this « Einstein nonseparability » and the nonlocality in Feynman’s « theory of positrons » is demonstrated through an analysis of the e+e+ annihilation into two photons. Thus the Einstein paradoxcorresponds, in the « new wavelike probability calculus », to the Loschmid and Zermelo sort of paradox in the old probability calculus. That is, it contrasts theintrinsic time symmetry existing at the elementary level to thefactlike macroscopic time asymmetry. Our discussion deliberately by-passes the hidden-variable problem, our model in this being Einstein’s by-passing of the mechanical aether when proposing special relativity. We believe that here today, like there in 1905, the problem istayloring the wording after the (operationally good)mathematics. Moreover, that the change in paradigm, which is needed, comes through a victory of formalism over modelism.

Nonexistence of the Aharonov-Bohm effect.—II: Discussion of the experiments

Abstract: SummarySome theoretical points of a previous paper on the same subject are further developed. In particular, it is shown that 1) the elementary treatments of the Aharonov-Bohm effect are vitiated by a false conception of the electron wave phase; 2) the Aharonov-Bohm effect is a consequence of an improper choice of the initial condition, or—alternatively—of the choice of an improper Green's propagator for the initial wave function. Then, the most significant experiments on the Aharonov-Bohm effect are discussed; it is shown that they are not probative, and a simple explanation is proposed.RiassuntoSi rendono espliciti taluni aspetti teorici di un'argomentazione sviluppata in un precedente lavoro sul medesimo problema. Si discutono poi i più significativi esperimenti sull'effetto Aharonov-Bohm, si dimostra che essi non sono probanti e se ne propone una semplice interpretazione.

Classical solutions for fermionic models

Abstract: Classical solutions for conformal invariant fermion-fermion interaction in two dimensions are given and their invariance properties are discussed. A possible generalization to four dimensions is given and corresponding instanton- and meron-like solutions are found. It turns out that these are a natural generalization of two-dimensional ones.

Discrete version of the nonlinear Schrödinger equation with linearlyx-dependent coefficients

Abstract: In this paper we discuss the differential-difference analog of the nonlinear Schrodinger equation with variable coefficients. The behaviour of the single-soliton solution is thoroughly investigated and the continuum limit is tersely derived.

Effects of coulomb repulsion in the inner-shell ionization cross-section by protons, deuterons and alpha-particles

Abstract: A critical survey has been made of the currently accepted BEA theory for inner-shell atomic-ionization processes. This review has led to the introduction of an effective ion energy which accounts for the slowing-down of the ion in the nuclear Coulomb field. The effect of the ion deflection, also due to the nuclear Coulomb field, is analysed. Relativistic effects in the collision of ions withK-shell electrons have been taken into account. A tentative qualitative explanation for the experimentally observed nonexistence of a threshold energy for ionization is given in the framework of the BEA theory. Ionization cross-sections for Rb, Sr, Zr, Cd, In, Sb, W by protons in the energy range from 500 keV to 3 MeV have been measured. Also measurements of ionization cross-sections by deuterons in the energy range from 800 keV to 2.6 MeV on Rb, Sr, Zr, Cd, Sb and by He ions in the energy range from 1.4 MeV to 2.8 MeV on Cd and Sb have been performed. Results are compared with those of other authors and in the context of the corrections introduced in the BEA theory.

The charge densities and single-particle structure of the even zirconium isotopes

Abstract: The charge densities of the zirconium isotopes 90, 92 and 94 are calculated by summing the squares of the proton wave functions in a one-body potential whose parameters are adjusted to give the experimental centroid energies. The squared wave functions are weighted by the single-particle occupation numbers. Accurate fits are obtained to the charge densities, and their differences are interpreted in terms of a simple model. It is also found that the radii of the potentials show significant departures from theA1/2 variation along the isotopic sequence.

Renormalization of Yang-Mills theory developed around an instanton

Abstract: We define the perturbation theory of Yang-Mills theory developed around an instanton. This needs for a proper treatment of the zero modes. The generalized Faddeev-Popov determinant mixes the contributions of the gauge, translations and dilatations zero modes; this difficulty necessitates the introduction of new ghosts. The existence of Feynman rules and a proper renormalization scheme are settled. Slavnov identities are proved; they allow us to show the independence of the theory from the parameters introduced to deal with the zero modes. At last, fermions are introduced and the framework is extended to QCD.

Computer simulations of Čerenkov light from large cosmic-ray showers

Abstract: Detailed computer simulations have been made for the air Cerenkov radiation produced in large cosmic-ray showers. The hadron cascade employed in the air shower simulation incorporates Feynman scaling; primary particles ranging in mass from protons to iron nuclei are considered. The simulation results compare well with recent measurements of the average characteristics of Cerenkov light from large cosmicray showers made with a synchronized array of fast photomultipliers at the Haverah Park EAS array; satisfactory overall agreement is found between the observations and the predictions for showers of primary energy (≈2·1017÷≈2·1018) eV having their electron cascade maximum at depths in the atmosphere of (≈680÷≈770) g cm−2. For the cascade model employed here these depths of maximum arise for a heavy primary mass composition.

Weyl and Conformal Covariant Field Theories

Abstract: It 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.

Distribution properties of the channel interactions inN-body scattering and applications

Abstract: We derive several classes of distribution properties for the channel internal and external interactions, as well as for generalized residual interactions, in the framework of theN-body scattering theory An essential feature of our distribution properties is that all coefficients are unity (natural distributions). We give several examples of the great advantages coming from the employment of the natural distributions in practical applications. Several classes of cluster expansions are derived for the channel resolvent operators and the Hepp-Narodetskii-Yakubovskii expansion is proved in a simple algebraic way. We present compact procedures leading to both the Sloan-Bencze-Redish equations and the Faddeev-Yakubovskii equations with artificial indices in the unknowns. We consider also many types of decompositions for the fullN-body scattering wave functions and, finally, we present general operatorial reversion properties for linked-cluster strings of resolvents and interactions.

Experimental confirmation of the 1100 structure and first observation of the leptonic decay of the ρ'(1250)

Abstract: We have extended our survey of the reaction γ+p→p+e++e− by collecting 20 000 additional e+e− pairs in the invariant-mass region 900

Charge density and single-particle structure: the nuclei39K,40Ca and48Ca

Abstract: The charge distributions of39K,40Ca and48Ca are calculated by summing the squares of the proton wave functions in a one-body nonlocal potential, whose parameters are adjusted to give the experimental centroid energies of the single-particle states. The squared wave functions are weighted by occupation numbers. The connection between the 2p-state occupation numbers and the diffuseness parameter of the potential is studied for the present nuclei and58Ni, whose density was calculated in a previous work. A good agreement with the «model indenendent» density is found.

On a relativistic model of the electron

Abstract: This paper aims at introducing an electron model derived from a theory previously developed by us for the classical electron, and then extended to the quantal case, based on the introduction of the chronon. Such a theory, besides the «macroscopical» motion of the particle, considers internal «microscopical» motions to which the «structure» of the electron is possibly related. This problem is approached with a procedure based on group theory, from which one derives that a space-time microuniverse of the De Sitter type, where the «internal motions» of the electron take place, can be associated with the electron. The intrinsic properties of the particle are originated by those motions. The description of the particle by an observer is given by means of the geodetical projection of the De Sitter space-time on a flat variety, consisting of a piece of the Minkowski space-time called Castelnuovo universe. In this variety the electron behaves as a 3-dimensional oscillating microcosmos reducing to a point at the extremes of any fundamental interval of proper time, when the macroscopical motion of the particle is defined. For such a motion, the electron can be considered as a point particle moving in the ordinary Minkowski space-time. It is also shown how the internal motion of the free electron associates to this particle of rest massm0 an intrinsic energym0c2, given by the kinetic energy of the electron itself, and an intrinsic magnetic moment µа=(1/4π)(e3/e0c2) equal to the first approximation of the anomalous magnetic moment predicted by Schwinger's quantum electrodynamics. Finally, we note that the present model of the electron affords a promising start toward the understanding of the meaning of the fine-structure constant.

Bounds on the total scattering cross-section forN-body systems

Abstract: We consider quantum-mechanical nonrelativisticN particle scattering systems with pair potentials decreasing at infinity more rapidly thanr−2. Let\(\bar \sigma _\alpha \left( \lambda \right)\)% MathType!End!2!1! be the total scattering cross-section, at energy λ, for scattering initiated in a two-body channel α. We derive explicit bounds, in terms of the pair potentials, for weighted averages of\(\bar \sigma _\alpha \left( \lambda \right)\)% MathType!End!2!1! over a range of energies and discuss some interesting features of these bounds, in particular their implications for the high-energy behaviour of\(\bar \sigma _\alpha \left( \lambda \right)\)% MathType!End!2!1!

A study of the Λπ-pd final state produced in K--meson interactions at rest in helium

Abstract: Results are presented of a bubble chamber study of K−-meson interactions at rest in helium leading to the Λπ−pd final state. It is found that (75±1)% of this final state results from the two-step mechanism of internal Σ-Λ conversion via processes such as\(K^ - {\mathcal{N}} \to \Sigma \pi \) followed by\(\Sigma {\mathcal{N}} \to \Lambda {\mathcal{N}}\). The experimental results are compared to the predictions of a double-impulse model, in which a contribution has been included from a Σ-Λ conversion process involving two nucleons in order to reproduce the baryon momentum spectra. The model is capable of explaining the features of the invariant-mass distributions of the finalstate particles without invoking resonance production.

Energy-momentum tensor of extended relativistic systems

Abstract: A general expression for the energy-momentum tensor of a system ofN interacting relativistic particles is obtained. In order to get this result, we analyse a particular model by constructing a coupling to an external gravitational field. The result obtained in this way is then generalized to an arbitrary situation. By studying the singularities of the energy-momentum tensor it is possible to get a clear understanding of the physics underlying the action-at-a-distance models.

The identification of a cascade hypernucleus

Abstract: In a systematic search for rare hypernuclear species in nuclear emulsion exposed to 3.0 GeV/c K−-mesons at the CERN PS, an event with three connecting stars has been observed. The two secondary stars are most probably due to the decay of a cascade hypernucleus according to the following channel: \(_\Xi ^{13} - C \to {}_\Lambda ^8 Be + {}_\Lambda ^5 He + Q\). The binding energy of the ÷-hypernucleus is \(B_{\Xi - } \left( {_{\Xi - }^{13} C} \right) - \left( {18.1 \pm 3.2} \right)\) MeV.

25 keV-neutron capture cross-sections

Abstract: By using the filtered beam of 25 keV neutrons from the reactions of the Bhabha Atomic Research Centre, isotopic capture crosssections for 19 nuclides in the mass regionA=51 to 187 have been measured. These measured cross-sections have been discussed in the light of s (slow) process nucleosynthesis.

Singularity analysis ofN-body scattering wave functions

Abstract: A thorough singularity analysis of scattering wave functions in theN-body problem is carried out. Operating on the basic Lippmann-Schwinger-Glockle-Tobocman equations and resorting to a general reversion property for linked-cluster strings of channel resolvents and interactions, we explicitly exhibit the sources of the primary singularities ofN-body scattering wave functions. We introduce complete sets of eigenstates of the two-cluster channel Hamiltonians and we arrive at momentum-space representations for two-cluster wave function components, where all the primary singularities appear in separate terms. By means of simple algebraic procedures we show that appropriate sums of the residues at the physical poles lead to the physical transition amplitudes for elastic/rearrangement, partial and total break-up processes.

On the general form of the double and triple angular correlation following the sequential decay of the heavy reaction products

Abstract: The general form of the double and triple differential cross-sections for the sequential three-body reaction X(a,b) Y(c)Z and four-body reaction X(a,b)Y(c)Z(f)R, respectively, are derived in the one-level excitation hypothesis. The transition amplitudes for the sequential processes are related to the scattering matrixS. Moreover, theoretical expressions for the b-c angular correlation are given under the hypothesis that the excited and partly polarized nucleus Y is produced in heavy-ion deeply inelastic collisions.

The gravitational charge 1/2 $$\sqrt {hc} $$ as a unifying principle in physicsas a unifying principle in physics

Abstract: We show in this paper that the basic quantization condition 4Gm2/c=nℏ, which was deduced previously from the Weyl principle of gauge invariance, as well as from the general-relativistic 2-body problem, leads to a particle with gravitational charge 1/2\(\sqrt {hc} \). It has the following properties: 1) It is a mini-black-hole; 2) it gives a natural gravitational cut-off for otherwise divergent self-energy calculations; 3) it represents a single quantum of actionh and hence is an ensemble of fluctuating gravitational fields in its lowest quantum state; 4) since its Bekenstein entropy is justk, to within a factor of the order of 1, it gives a physical meaning to the otherwise mysterious Boltzmann constant; 5) it leads to a statistical mechanics of the interior of a macro-black-hole of massM in the sense that it yields the quantityN=M/m as the number of distinct particles within the black hole and the quantityN2/2 as its number of excitable interior degrees of freedom; 6) it yields a simple formula for the square root of the fine-structure constant (accurate to better than 1 part in 1000) as the ratio of the number of degrees of freedom of the electromagnetic field with source to the number of degrees of freedom of the gravitational field with source; 7) it leads to a formula for the masses of leptons, mesons and baryons; 8) it permits one to express both the weak- and strong-coupling constants as small powers of the fine-structure constant.

Meson transfer to atoms and molecules

Abstract: The role of the electron distribution in meson transfer reactions is studied. It is found that the transfer cross-sections from excited states are strongly dependent on the chemical structure.