Generalized Dispersion Relations Research Articles

Dispersion relations and sum rules for the ellipsometric function

A simple Lorentz oscillator model for the dielectric function is applied to the generalized dispersion relations and the sum rules for the ellipsometric function. Numerical results obtained illustrate the complementary behavior of the ellipsometric parameters, ψ and Δ, linked by the dispersion relations, as functions of photon energy. Comparisons are made between the convergence of the sum rules for ψ and Δ and the previously known sum rules for the dielectric function.

Comments on the dispersion relations for the complex refractive index of circularly and elliptically polarized light*

The generalization to circularly polarized modes of the Kramers-Kronig relations for the complex refractive index is discussed in terms of the analyticity of the index to clarify the physical basis of the generalized dispersion relations. A compact form for the circular-mode dispersion relations is obtained that is particularly useful in treating dichroic effects and for deriving optical sum rules. The procedure is generalized to elliptically polarized modes. It is shown that the generalized dispersion relations must be used for the optical constants of elliptic modes that retain their ellipticity to arbitrarily small frequencies, while dispersion relations of the Kramers-Kronig form apply to elliptic modes that are linearly polarized in the limit of small frequencies.

Derivation and implications of rigorous absolute bounds for ππ partial waves up to 1 GeV

Generalized dispersion relations and axiomatic results are used to derive absolute upper bounds for the ππ partial waves in a complex energy domain containing the physical region up to 1 GeV. As applications, a new lower bound for the π 0 π 0 S-wave scattering length is given and some ambiguities in the connection between resonances and second sheet poles are removed.

New dispersion relations and their application to partial-wave amplitudes

After reviewing the commonly used dispersion relations, a systematic investigation of more generalized dispersion relations on parametrized curves in the Mandelstam plane fors-u crossing-symmetric amplitudes is made with the aim of obtaining dispersion relations which receive contributions from all three channels, however, in such a way that knowledge of the absorptive parts is only required in regions well inside the various Lehmann ellipses. In addition we require that the dispersion relations receive no contributions from kinematic singularities arising from the parametrization and that they allow partial-wave projections to be made in a relatively simple manner. It is found that dispersion relations on hyperbolic curves in the Mandelstam plane are a natural solution of the problem. The dispersion relations are written in a remarkably simple form similar to the usual fixed-t dispersion relation but with an additionalt-channel contribution. As an interesting application, we derive generalized partial-wave dispersion relations for elastic pion-nucleon scattering, where the left-hand cut contribution is explicitly given by convergent partial-wave series in the crossed channels.

Generalized Functions and Dispersion Relations in Physics

Fortschritte der PhysikVolume 14, Issue 1-12 p. 483-602 Article Generalized Functions and Dispersion Relations in Physics W. Güttinger, W. Güttinger Institute of Theoretical Physics, University of Munich MünchenSearch for more papers by this author W. Güttinger, W. Güttinger Institute of Theoretical Physics, University of Munich MünchenSearch for more papers by this author First published: 1966 https://doi.org/10.1002/prop.19660140114Citations: 84AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume14, Issue1-121966Pages 483-602 RelatedInformation

Generalized dispersion relations

General dispersion relations for reactionsa+b →a′+c+d have been obtained. The possible cases of (γ+p → 2γ+p) scattering have been indicated, for which dispersion relations do not contain unobservable range of energy.

Dispersion relations for fermions

Generalized dispersion relations for scattering of 2 fermions are derived in a way similar to that used for fermion-boson scattering. The 2-nucleon problem is discussed in particular. The relations are written for functions which can be expressed in terms of the phase shifts.