Pole Singularities Research Articles

Evidence for aJ = 0 fixed pole and Kronecker-delta singularity in pion Compton scattering

Evidence for aJ = 0 fixed pole and Kronecker-delta singularity in pion Compton scattering

Regge behaviour in an asymptotically free field theory

We consider the high energy behaviour at fixed momentum transfer of ϕ 3 theory in six dimensional space-time, as the simplest example of an exactly renormalisable asymptotically free theory. We find that the damping in transverse momentum of the full theory is sufficiently strong to give rise to moving Regge pole singularities, in contrast to a fixed-point theory which would naturally lead to a fixed square-root branch point.

Primary Singularities, Asymptotic Wave Functions and Unitarity in the Three-Body Problem

This paper studies the singular pole structure present in the momentum space three-body-scattering wave functions. We prove that this structure alone is entirely responsible for the asymptotic behavior in coordinate space. We are also able to prove, without further assumptions, that the residues of each of the singularities in the wave function must be physical scattering amplitudes. We extend our study of these primary poles in three-body physics by using the singularity structure to obtain a derivation of the on-shell unitarity relations.

The signatured Froissart-Gribov continuation of multiparticle amplitudes to complex helicity and angular momentum

Signatured “Froissart-Gribov” continuations in the complex angular momentum and helicity planes of a multiparticle amplitude are defined on the basis of the expected singularity structure of such amplitudes. Multiple Sommerfeld-Watson transformations of the associated partial-wave expansions are also described. A five-particle amplitude with normal threshold and pole singularities in each invariant variable is considered in detail.

Collective Instabilities and Waves for Inhomogeneous Stellar Systems. II. The Normal-Modes Problem of the Self-Consistent Plane-Parallel Slab

view Abstract Citations (23) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Collective Instabilities and Waves for Inhomogeneous Stellar Systems. II. The Normal-Modes Problem of the Self-Consistent Plane-Parallel Slab Mark, James W. K. Abstract Studies have been made of the normal modes of instabilities and waves for models of inhomogeneous, nonrotating stellar systems whose basic equilibrium has one-dimensional planar symmetry (slabs) while the perturbations are not restricted to this symmetry. Comparisons are also made with gaseous slabs, the energy principle, and the Hartree-Fock operator principle. The perturbations separate into modes even and odd in the spatial coordinate parallel to the density gradient. For even modes, the gravitational instability has been isolated under more general conditions than in a previous derivation that used the energy principle. A two-stream instability is identified at long wavelengths as an even mode. Bending-type odd modes are also found. For nearly isotropic velocity distributions, this bending mode is a propagating, neutral (or slightly damped) wave, while for large velocity anisotropies, the Kelvin-Helmholtz (fire-hose) instability is recovered. For initial-valued problems involving this inhomogeneous equilibrium, each of these modes gives a pole singularity in the Laplace transform of the time behavior. Publication: The Astrophysical Journal Pub Date: November 1971 DOI: 10.1086/151162 Bibcode: 1971ApJ...169..455M full text sources ADS | Related Materials (1) Part 1: 1970ApJ...160..471K

Properties of Mandelstam Cuts

The properties of Mandelstam cuts are discussed which can be deduced from expressions suggested by Feynman integrals together with an understanding of the singularity structure of real integrals. The suggestion of Schwarz about their "switching on and off" properties is confirmed, and some expressions for discontinuities are elucidated. The existence of a pole singularity underneath the Reggeon-particle and normal threshold cuts is demonstrated, and the importance of its role in eliminating the Gribov-Pomeranchuk essential singularity is emphasized. This property is also explored in terms of the Feynman-integral model, and the dangers and subtleties of calculations based on orders of the third spectral function are exhibited.

Space and Time inS-Matrix Theory

Basic elements of a theory of measurements of space-time correlations are developed within the framework of a strictly mass-shell $S$-matrix theory. The "$i\ensuremath{\epsilon}$ rule" for the resolution of pole singularities is derived from a macroscopic mass-shell causality condition. The experimental and theoretical significance of form factors is discussed from the point of view of analytic $S$-matrix theory. They are defined as constructs of mass-shell functions, and the conditions under which they can be ascribed approximate experimental significance are examined. The possibility that asymptotic field theory is contained within analytic $S$-matrix theory is briefly discussed.

Resonance Scattering of Phonons by Molecular Impurity Centers

The scattering of phonons at polyatomic (molecular) impurity centers cannot be handled by the regular Lifshitz method because of the additional degrees of freedom. A method is presented which makes it possible to eliminate the molecular coordinates by means of a molecular Green's function. This Green's function defines an effective disturbance in the lattice system with singular poles at the molecular frequencies. Thus the low rank $t$ matrix of the scattering formalism, defining the scattering amplitude, has sharp resonances near the molecular frequencies. The abstract scattering formalism is applied to a simple example which exhibits the influence of librational modes of a molecule with strong internal bindings on phonon scattering. The $t$ matrix for the chosen model is diagonalized by complete group theoretical reduction and reveals the structure of the molecular resonances explicitly. It is found that the resonance is very sharp if the molecular frequency is much smaller than the Debye frequency, and decreases for higher frequencies.

Regge Poles and Complex Singularities

The analyticity in complex angular momentum for the case in which complex singularities are present in doublespectral representations of scattering amplitudes is studied. The simple example considered is SIGMA SIGMA scattering. It is shown that Regge continuation exists and has the same qualitative characteristics as for the case of no complex singularities. In particular, no direct connection is found between the presence of complex singularities and the existence of the branch cuts in angular momentum. (auth)