Mesonic degrees of freedom in nuclei and the definition of meson-exchange currents

We describe the nucleus by a meson-nucleon system. Starting from a covariant field theoretical Hamiltonian we derive an effective Schrödinger equation for the nucleonic components. The meson-exchange currents are then defined unarbitrarily by an effective operator (current) in the space of the nucleonic components. The advantage over theS-matrix method [1] is discussed. In the nonrelativistic limit the meson-current as well as the seagull (pair) current agrees with theS-matrix result. Recoil and wavefunction orthogonalization cancels completely in this limit.     

Construction ofS-matrix from scattering data

A method of construction of the scatteringS-matrix from scattering data is proposed. The scattering matrix is expressed in the form of a rational fraction and takes fully into account the analytic properties of theS-matrix. The method generates a unique and stable analytic continuation of theS-matrix into the complex energy plane. The method is applied to calculation of energy and widths of several resonances in nuclear and atomic physics. Its efficiency is compared with some recently proposed methods.     

Hidden Yangians in 2D massive current algebras

We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of the Yangians. We show how the noncocommutativity of the Yangians is related to the non-locality of the currents. We discuss the implications of the existence of non-local conserved charges on theS-matrices.Laboratoire de la Direction des sciences de la matière du Commissariat à l'énergie atomique     

Chiral electromagnetic meson exchange currents

Properties of electromagnetic isovector meson exchange currents are discussed starting from the concept of chiral symmetry and vector meson dominance. The 4-currents are constructed in the framework of theS-matrix method and satisfy the current conservation also at the relativistic level. The comparison with the standard approach is made in detail. The case when only current conservation and Lorentz invariance are taken into account is also considered. Cross sections are compared with the new data.Lectures held at the Indian Summer School on Electromagnetic and Weak Interactions of Particles with Nuclei, Sázava, Czechoslovakia, 6–11 September 1992I am indebted to the organizers for inviting me to the school.     

Study of theS-matrix near bound states in the continuum

The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.     

Hypernuclear properties derived from the Jülich hyperon-nucleon interaction (in comparison with the Nijmegen interactions)

TheG-matrix interactions are derived from the Jülich YN interaction models A and B, and compared with those from the Nijmegen models. The DDHF calculations for heavy A hypernuclei and the shell-model analysis for spin-doublet states of light hypernuclei are performed by use of theG-matrix interactions. It is demonstrated that the OBE models can be tested by the hypernuclear calculations.     

Z 4-symmetric factorizedS-matrix in two space-time dimensions

The factorizedS-matrix with internal symmetryZ ₄ is constructed in two space-time dimensions. The two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations. The solution of factorization equations can be expressed in terms of elliptic functions. TheS-matrix contains the resonance poles naturally. The simple formal relation between the general factorizedS-matrices and the Baxter-type lattice transfer matrices is found. In the sense of this relation theZ ₄-symmetricS-matrix corresponds to the Baxter transfer matrix itself.     

The local potential approximation for the Brueckner G-matrix and a simple model of the scalar-isoscalar Landau-Migdal amplitude

The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet ^1S and triplet ³ S + ³ D channels. The complete Hilbert space is split into two domains, the model subspace S₀, in which the two-particle propagator is calculated explicitly, and the complementary one, S', in which the local potential approximation is used. This kind of local approximation was previously found to be quite accurate for the ^1S pairing problem. A set of model spaces S ₀(E ₀) with different values of the energy E₀ is considered, E₀ being the upper limit for the single-particle energies of the states belonging to S₀. The independence of the G-matrix on E₀ is assumed as a criterion for the validity of the local potential approximation. It turns out that such an independence holds within few percents for E ₀ = 10-20 MeV, for both channels under consideration. The G-matrix within the local potential approximation is used for justifying a simple microscopic model for the coordinate-dependent scalar-isoscalar component f (r) of the Landau-Migdal amplitude in terms of the free T-matrix. Received: 2 November 2001 / Accepted: 4 January 2002     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

On the regular holonomic character of theS-matrix and microlocal analysis of unitarity-type integrals

The previously proved results that every analytically renormalized Feynman integral is a regular holonomic function suggests that theS-matrix should be locally expressible as an infinite sum of regular holonomic functions. A regularity propertyR is formulated that expresses the condition that theS-matrix be locally expressible near each physical pointp as a convergent sum of regular holonomic functions, with each term enjoying some of the regularity properties of a corresponding Feynman integral. This propertyR holds at every physical pointp that has yet been analyzed by the methods of axiomatic field theory orS-matrix theory. Some analyticity properties of unitarity-type integrals are then examined under the assumption that theS-matrix satisfies propertyR and a weak integrability condition. These results rest heavily on some recently proved properties of regular holonomic functions.     

Analytic structure in λ of theS-matrix for strongly singular potentials

The asymptotic behaviour in the -plane of solutions of the Schrödinger equation for scattering on singular potentials is investigated. The asymptotic behaviour of the Jost functions and theS-matrix is obtained. Furthermore, the general analytic form in the -plane of the Jost functions and theS-matrix is established. Some properties of the distribution of poles of theS-matrix are proved.On leave of absence from the Institute Ruder Bokovi, Zagreb, and the Zagreb University, Yugoslavia.     

Existence of the scattering matrix for the linearized Boltzmann equation

Following Hejtmanek, we consider neutrons in infinite space obeying a linearized Boltzmann equation describing their interaction with matter in some compact setD. We prove existence of theS-matrix and subcriticality of the dynamics in the (weak-coupling) case where the mean free path is larger than the diameter ofD uniform in the velocity. We prove existence of theS-matrix also for the case whereD is convex and filled with uniformly absorbent material. In an appendix, we present an explicit example where the dynamics is not invertible onL ₊ ¹ , the cone of positive elements inL ¹.A. Sloan fellow; research partially supported by the U.S. NSF under Grant GP 39048     

The invariance of theS-matrix under point transformations in renormalized perturbation theory

We give a simple proof of the invariance of theS-matrix under point transformations of the fields in renormalized perturbation field theory.     

K −-Proton atomic transitions

The relation between theK ^}-P scattering length and the X-ray spectrum for the 2p → 1s electromagnetic transition inK ^?-P atoms is examined. A coupled-channel potential model is used to explicitly calculate the energy of theS-matrix pole in the 1s channel, which is then compared with the energy obtained from the scattering lengths via the standard equation. The X-ray spectrum is calculated and compared with the Lorentzian shape associated with the complex energy of theS-matrix pole. In addition, theK ^?p branching ratios are compared at threshold and at the complexS-matrix pole energy.     

Causality in quantum field theory with nonlocal interaction

It is proved that theS-matrix satisfies the Bogolubov microcausality condition in each order in perturbation theory in a quantum field theory with nonlocal interaction, where the nonlocality is introduced with the help of form factors being entire analytical functions of the order 1/2.     

Dependence of the S-matrix on the choice of field variables in the effective Lagrangian

The dependence of the on-shellS-matrix on the change of the Lagrangian induced by a nonlinear substitutionF() is investigated by means of a graphical analysis. A cancellation mechanism is found and used to show that the tree approximation of theS-matrix is independent of such a substitution and that the Jacobian of the substitution has to be introduced in order to cancel a new class of singular one-loop graphs and to recover the primaryS-matrix at the one-loop level.     

The spectral problem for theq-Knizhnik-Zamolodchikov equation and continuousq-Jacobi polynomials

The spectral problem for theq-Knizhnik-Zamolodchikov equations for at arbitrary non-negative levelk is considered. The case of two-point functions in the fundamental representation is studied in detail. The scattering states are given explicitly in terms of continuousq-Jacobi polynomials, and theS-matrix is derived from their asymptotic behavior. The level zeroS-matrix is closely connected with the kink-antikinkS-matrix for the spin- XXZ antiferromagnet. An interpretation of the latter in terms of scattering on (quantum) symmetric spaces is discussed. In the limit of infinite level we observe connections with harmonic analysis onp-adic groups with the primep given byp=q ^–2.Work supported in part by the NSF: PHY-91-23780     

Analytic continuation of group representations-V

The connection between analytic continuation of group representations and analytic continuation of their matrix elements is discussed, together with some related problems concerning the group-theoretic nature of theS-matrix, and the asymptotic behavior of the special functions of mathematical physics.Work supported by U. S. Atomic Energy Commission     

Low-energy three-body scattering in a hyperspherical adiabatic basis

We propose a hyperspherical adiabatic formalism for the calculation of the 3-to-3S-matrix at low energy, for repulsive potentials, and use it then in a model calculation. That is for McGuire's model (3 particles in one dimension subject to repulsive delta-function interactions), we use analytical expressions for the hyperspherical adiabatic basis, the adiabatic coupling matrix elements, and eigenpotentials to obtain the first terms of the exactS-matrix analytically, in an expansion in powers of the wave number. We were able to associate the definite powers ofq in the expansion of theS-matrix to the corresponding inverse powers of in the expansions of the adiabatic eigenpotentials and coupling matrix elements. We investigate the effect of making the usual approximations found in the literature (extreme and uncoupled adiabatic approximations), when calculating the diagonal and off-diagonalS-matrix elements. Finally, we show that the coupled adiabatic equations uncouple as the energy goes to zero.     

Analyticity and ergodicity in the maximum-entropy approach to statistical nuclear reactions

In the maximum-entropy approach to statistical nuclear reactions one imposes naturally the constraints of unitarity and symmetry of theS-matrix, and of a fixed expectation value ofS. We show that the analytical structure of theS-matrix and the requirement that the problem be ergodic (so that energy averages can be replaced by ensemble averages) impose certain restrictions on the distribution of statisticalS-matrices. Some of these additional constraints are then imposed numerically in a two-channel calculation, and are shown to improve the results for the fluctuation cross sections, the elastic enhancement factor, etc.