Yennie Gauge Research Articles

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space

We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon-exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.

Radiative nonrecoil nuclear finite size corrections of order α(Zα)5 to the hyperfine splitting of S-states in muonic hydrogen

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order α(Zα)5 to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried–Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.

Second-order electron self-energy loop-after-loop correction for low-Z hydrogen-like ions

The second-order electron self-energy loop-after-loop correction is investigated for hydrogen-like ions in the region of low nuclear charge numbers Z. Both irreducible and reducible parts of this correction are evaluated for the 1s1/2-state within the Fried–Yennie gauge. We confirm the result obtained first by Mallampalli and Sapirstein. The reducible part of this correction is evaluated numerically for the first time and it is consistent with the corresponding analytical αZ-expansion.

Three-loop reducible radiative photon contributions to Lamb shift and hyperfine splitting

Corrections of order ${\ensuremath{\alpha}}^{3}{(Z\ensuremath{\alpha})}^{5}m$ to the Lamb shift and corrections of order ${\ensuremath{\alpha}}^{3}(Z\ensuremath{\alpha}){E}_{F}$ to the hyperfine splitting, generated by insertion of the three-loop one-particle reducible diagrams with radiative photons in the electron line, are calculated. The calculations are performed in the Yennie gauge.

One-loop electron vertex in Yennie gauge

We derive a compact Yennie gauge representation for the off-shell one-loop electron-photon vertex, and discuss it properties. This expression is explicitly infrared finite, and it has proved to be extremely useful in multiloop calculations in the QED bound state problem.

Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

The results and main steps of an analytic calculation of radiative-recoil corrections of order $\alpha(Z\alpha)^5(m/M)m$ to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our new result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.

Infrared behavior of Yennie gauge QED at two-loop order

We show, by explicit calculation, that the on-shell renormalization constants of Yennie gauge QED are infrared finite to two-loop order.PACS Nos.: 12.20.Ds and 11.10.Gh

Infrared behavior of Yennie gauge QED at two-loop order

Infrared behavior of Yennie gauge QED at two-loop order

Contribution of light-by-light scattering to the orders O(m alpha 8) and O(m alpha 8ln alpha ) orthopositronium decay rate.

The gauge invariant contribution of the six radiatively corrected light-by-light scattering processes to the decay rate of orthopositronium into three photons is calculated. The infrared-safe Yennie gauge is used for the loop photons. The relative order of ${\mathrm{\ensuremath{\alpha}}}^{2}$ part of our result, 9.0074(9)(${\mathrm{\ensuremath{\alpha}}}^{2}$/${\mathrm{\ensuremath{\pi}}}^{2}$)${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LO}}$, makes a 0.000350 \ensuremath{\mu}${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ contribution to the decay rate, thus reducing slightly the apparent discrepancy between the theoretical and experimental results. ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LO}}$ is the lowest-order decay rate. The analytically obtained relative order ${\mathrm{\ensuremath{\alpha}}}^{2}$ln \ensuremath{\alpha} part of our result, -${\mathrm{\ensuremath{\alpha}}}^{2}$ln(1/\ensuremath{\alpha})${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LO}}$, is in agreement with earlier evaluations.

One-loop vertex function in Yennie gauge QED

In this paper we give a convenient expression for the one-loop vertex correction in Yennie gauge QED. We use dimensional regularization to regulate ultraviolet and potential infrared divergences. We study the infrared behavior of the vertex correction in a class of simple covariant gauges, and verify that [beta]=2/(1[minus]2[epsilon]) is the appropriate choice for the gauge parameter of the Yennie gauge (where [ital n]=4[minus]2[epsilon] is the dimensionality of spacetime).

Radiative-recoil contributions to the Lamb shift

We consider the proton mass corrections to the radiative Lamb shift in hydrogen. A procedure is developed to incorporate these contributions in the standard approach for obtaining the nonrecoil shifts. An equation given by Grotch and Yennie is used as a starting point to describe the hydrogen atom. This equation includes the Coulomb and the convection potentials as well as the proton kinetic energy. The radiative corrections then produce the desired radiative-recoil contributions. The complete lowest order (..cap alpha..(Z..cap alpha..)/sup 4/ m/sup 2//M) contributions as well as part of the higher order (..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M) contributions are derived analytically in the so-called external field approximation. In order to obtain residual ..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M contributions, we then consider perturbation kernels involving the two-photon exchange diagrams which are not already included in the external field approximation calculation. This is done utilizing the Fried--Yennie gauge for the radiative photon and the Coulomb gauge for the exchanged photons. The behavior of the perturbation kernels in the low-momentum region of the exchanged photon is analyzed in considerable detail. For the evaluation of the energy shift, the integrals are carried out numerically. The ..cap alpha..(Z..cap alpha..)/sup 5/ m/sup 2//M contributionmore » beyond the usual reduced mass correction is ..delta..E/sub n/ = (..cap alpha..(Z..cap alpha..)/sup 5//n/sup 3/) m/sup 2//M(-1.574+(-0.415 +- 0.004)) delta/sub l//sub 0/. For the 2S/sub 1/2/--2P/sub 1/2/ Lamb shift in hydrogen, this amounts to a contribution of (-2.527 +- 0.005) kHz.« less

Infrared Behavior in a Model for Quantum Electrodynamics

In another paper, a particular solution of the Ward–Takahashi identity was set up as a model for quantum electrodynamics. The high energy behavior of the electron and photon propagators was investigated. The purpose of the present work is to investigate the asymptotic infrared behavior of the electron propagator near the mass shell in our model–theory. It is shown that, in general, it has a branch point, rather than just a pole at p2 = −m2, with the "singularity" being different from the known result of Abrikosov and Solov'ev, and coincides with theirs only in the gauge G = −1. The electron propagator, however, has rigorously a pole in the Yennie gauge.

Electromagnetic mass differences and the yennie gauge

Electromagnetic mass differences and the yennie gauge

Low-Energy—Theorem Approach to Single-Particle Singularities in the Presence of Massless Bosons

By the use of low-energy theorems, which follow from gauge invariance and analyticity assumptions, we determine the nature of the single-particle singularity of a meson propagator in the presence of the known massless bosons:Photons and gravitons. In addition to regaining the well-known results for covariant gauges in electrodynamics, we present new results for covariant gauges in gravity theory, and for radiation gauges in both electrodynamics and gravity theory. The gauges in which no infrared singularities are present are found: For covariant electrodynamics it is of course the Yennie gauge; for covariant gravity theory a similar gauge is given. In radiation gauges it is shown that Schwinger's new gauge has this desirable property for photons, and an analogous gauge is constructed for gravitons. It is established that in these gauges the single-particle singularity of the meson propagator becomes a simple pole.