Function In Quantum Electrodynamics Research Articles

Gravitational corrections to two-loop beta function in quantum electrodynamics

In this work, we use the framework of effective field theory to couple Einstein's gravity to quantum electrodynamics (QED) and determine the gravitational corrections to the two-loop beta function of the electric charge in arbitrary electrodynamics (Lorentz-like) and arbitrary (de Donder--like) gravitational gauges. Our results indicate that gravitational corrections do not alter the running behavior of the electric charge; on the contrary, we observe that it gives a positive contribution to the beta function, making the electric charge grow even faster.

Log expansions from combinatorial Dyson\u2013Schwinger equations

We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling constant alpha and a logarithmic energy scale L—a reordering of terms as G(alpha ,L) = 1 pm sum _{j ge 0} alpha ^j H_j(alpha L) is the corresponding log expansion. In a first part of this paper, we derive the leading log order H_0 and the next-to^{(j)}-leading log orders H_j from the Callan–Symanzik equation. In particular, H_j only depends on the (j+1)-loop beta -function and anomalous dimensions. In two specific examples, our formulas reproduce the known expressions for the next-to-next-to-leading log approximation in the literature: for the photon propagator Green’s function in quantum electrodynamics and in a toy model, where all Feynman graphs with vertex sub-divergences are neglected. In a second part of this work, we review the connection between the Callan–Symanzik equation and Dyson–Schwinger equations, i.e., fixed-point relations for the Green’s functions. Combining the arguments, our work provides a derivation of the log expansions for Green’s functions from the corresponding Dyson–Schwinger equations.

Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics

A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories, characterized by an infinite number of Kaluza-Klein fields, one-loop amplitudes involve discrete as well as continuous sums, $\sum^\infty_{n=1}\int d^4k$, that could diverge. Using dimensional regularization, we express such sums as products of gamma and Epstein functions, both defined on the complex plane, with divergences arising from poles of these functions in the limit as $ D \to 4$. Using the analytical properties of the Epstein function, we show that the ultraviolet divergences generated by the Kaluza-Klein sums can be consistently renormalized, which means that the corresponding renormalized quantities reduce to the usual ones of QED at the limit of a very large compactification scale $R^{-1}$. The main features of QED at the one-loop level were studied. We use the mass-dependent $\mu$-scheme to calculate, in QED with an arbitrary number $n$ of extra dimensions, a beta function fulfilling all desirable physical requirements. We argue that in this type of theories, with a large mass spectrum covering a wide energy range, beta functions should not be calculated by using mass-independent renormalization schemes. We show that the beta function is finite for any energy $\mu$. In particular, it reduces to the usual QED result $e^3/12\pi^2$ for $m\ll \mu \ll R^{-1}$ and vanishes for $m\gg \mu$, with $m$ the usual fermion mass. Throughout the work, the decoupling nature of all our results obtained from the analytical properties of the Epstein function is stressed.

New aspects of quantum electrodynamics on electronic structure and dynamics.

Application of Alpha-oscillator theory to quantum electrodynamics (QED) solves the mystery (Feynman) of the double-slit phenomenon involved in the foundation of quantum mechanics (QM). Even if with the same initial condition given, different spots on the screen can be predicted deterministically with no introduction of hidden variables. The interference pattern is similar to, but cannot be reproduced quantitatively by, that of the QM wave function, contrary to many-years-anticipation: a new prediction, awaiting experimental test over and above the Bohr-Einstein gedanken experiment. The general proof has already been published in Ref. [3a] and the concrete numerical algorithm of the extended normal mode technique for concrete trajectory of one electron in Ref. [3b]. In this article, (1) the new "interpretation" of the QED wave function is given in section "Interpretation of Wave Function in QED": the QED wave function used in the extended normal mode technique gives probability density distribution function of the initial values of trajectories. Moreover, (2) for the sake of demonstration of this new interpretation, the time-independent stationary state QM wave function is substituted to the QED wave function in section "Internal Self-Stress of Energetic Particles": the QED wave function is realized by internal self-stress revealed as energy density at the initial conditions. The renewed energy density is applied to study a unified scheme for generalized chemical reactivity. This is a new kind of chemical force acting in between electrons not in between nuclei. This paves a way for more advanced time-dependent simulation of electronic structure and dynamics in chemical reaction dynamics by tracing trajectories of many electrons. © 2018 Wiley Periodicals, Inc.

Symmetric point four-point functions at one loop in QCD

We evaluate the quartic ghost and quark Green's functions as well as the gluon-ghost, gluon-quark and ghost-quark four-point functions of quantum chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green's functions in quantum electrodynamics are also provided.

Schwinger–Dyson equation in Minkowski space beyond the IE approximation

We investigate the properties of fermion mass functions in quantum electrodynamics calculated by the Schwinger-Dyson equation in the strong coupling region, in which the loop integration is performed in Minkowski space. The calculated results without the instantaneous exchange approximation are compared with those obtained by integration in Euclidean space.

Exact asymptotic form for the β function in quantum electrodynamics

It is shown that the asymptotic form of the Gell-Mann-Low function in quantum electrodynamics can be determined exactly: β(g) = g for g → ∞, where g = e 2 is the running fine-structure constant. This solves the problem of electrodynamics at small distances L (for which dependence g ∞ L −2 holds) and completely eliminates the problem of “zero charge.”

Quantum electrodynamics at large distances. III. Verification of pole factorization and the correspondence principle.

In papers I and II it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the terms of the remainder are here shown to have singularities on the pertinent Landau singularity surface that are weaker than those of the distinguished part. These remainder terms therefore vanish, relative to the distinguished term, in the appropriate macroscopic limits. This shows, in each order of the perturbative expansion, that quantum electrodynamics does indeed satisfy the pole-factorization and correspondence-principle requirements in the case treated here. It also demonstrates the efficacy of the computational techniques developed here to calculate the consequences of the principles of quantum electrodynamics in the macroscopic and mesoscopic regimes.

The Sudakov form factor beyond the leading logarithmic approximation

We present the general form of the asymptotic behavior of the massless electron-photon vetex function in quantum electrodynamics in the limit whereq2, the virtual mass of the photon, becomes large. All the logarithms inq2 are taken into account, whereas inverse powers ofq2 are neglected. In contradistinction to previous investigations we consider the off-shell vertex function and work in the Feynman gauge. Extensive use is made of the α-representation of Feynman integrals.

Infrared asymptotics of the three-point Green's function in a charge-symmetric model

Equations have been obtained, in a logarithmic approximation, for the infrared asymptotic behavior of a vertex function in a model of a massive isospinor field interacting with a massless isovector one. The particular solution obtained indicates the essential absence of infrared asymptotics of the vertex function in quantum electrodynamics.

Infrared Phase Factors in Quantum Electrodynamics

Infrared singularities in Green functions in quantum electrodynamics are studied from the point of view of path-ordered phase factors in an infrared approximation. The singular exponential factor in the vertex part is reproduced by a simple calculation of the phase factor. The result is compared with the one obtained by the Kulish-Faddeev model.

Two-point Green's functions in quantum electrodynamics at finite temperature and density

One-particle propagators of the relativistic electron-positron gas are systematically investigated. With the nonvanishing chemical potential the neutrality of the whole system is secured by a uniformly charged classical background described by a classical current J μ . Due to the translational invariance of this model it is natural to investigate the properties of the propagators in the momentum space. The Fourier-transforms of the Green's functions have been expressed in terms of the generalized spectral Lehmann representation and the second-order spectral functions of the photon and electron propagators have been found. The matter-dependent part of the propagator is finite and only the vacuum part has to be renormalized with the use of standard renormalization counterterms. The singularities of the gauge-independent photon propagator have been further investigated with the use of the spectal representation and nonperturbative expressions for the spectrum of collective excitations have been obtained. In the second order of perturbation they reproduce the asymptotic formulas at T → 0 and T → ∞ cited previously in the literature. In particular, the relativistic plasma frequency (photon effective mass) has been expressed in a simple form in terms of the integrals over the spectral functions. Our formulas for the relativistic plasmon mass squared Ω 2 exhibit an interesting property that at some temperature and density Ω 2 should become negative. However, simple estimates show that this phenomenon occurs at highly nonrealistic temperatures of the order of e 137, i.e., in the region where the perturbation theory fails. The damping of the collective excitations is also considered.

Two-point Green's functions in quantum electrodynamics at finite temperature and density: Adam Bechler. Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland

Two-point Green's functions in quantum electrodynamics at finite temperature and density: Adam Bechler. Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland

Spectral ansatz in quantum electrodynamics: Spectral functions and gauge transformations

Using the ansatz of Delbourgo and Salam for the vertex function in quantum electrodynamics, we find approximations to the spectral functions of the electron propagator for covariant gauges. The consistency with the integral relations for the change of the exact spectral functions under covariant gauge transformations is investigated. The approximated spectral functions appear not to be gauge covariant in general.

Eighth-order contribution to the Callan-Symanzik function in quantum electrodynamics from fourth-order vacuum polarization insertions

We have calculated the contribution to the Callan-Symanzik function β(α) in quantum electrodynamics from the Feynman diagrams corresponding to fourth-order vacuum polarization corrections to the fourth-order vacuum polarization. The result is (α/π) 4 [− 61 1296 + ( 2 27 )π 2 + ( 1 2 ) ζ (3)] = 1.285 (α/π) 4) .

On the infrared singularities of Green's functions in quantum electrodynamics

We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.

Short-distance analysis of the triangle anomaly in quantum electrodynamics

The connection between the existence of a non-zero triangle anomaly and the short-distance properties of Green functions in quantum electrodynamics (QED) are re-examined. We find that part of a previous analysis must be corrected, and we record some additional observations on the internal consistency of finite theories of QED.

On the infrared singularities of green's functions in quantum electrodynamics: Nicolas Papanicolaou. Department of Physics, New York University, New York, New York 10003

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Asymptotic Behavior of the Vertex Function in Quantum Electrodynamics

Using recently developed infinite-momentum techniques, we study the asymptotic behavior of the three-point function in quantum electrodynamics (massive photons) by summing the leading behavior of the perturbation series. We find that the leading diagrams are those in which photons are exchanged in all permutations across the external photon insertion. When the fermion lines are on-shell, we confirm an earlier speculation of Jackiw based on a fourth-order calculation, namely, that the vertex exponentiates in the form $\overline{u}({p}_{f}){\ensuremath{\Lambda}}^{\ensuremath{\mu}}u({p}_{i})=\overline{u}({p}_{f}){\ensuremath{\gamma}}^{\ensuremath{\perp}}u({p}_{i}){e}^{\ensuremath{-}\ensuremath{\Phi}}$, where $\ensuremath{\Phi}=(\frac{{e}^{2}}{16{\ensuremath{\pi}}^{2}}){\mathrm{ln}}^{2}(\frac{{Q}^{2}}{{\ensuremath{\mu}}^{2}})$. In a fashion which is reminiscent of eikonalization in a scattering process, $\ensuremath{\Phi}$ is characteristic of single-photon exchange across the vertex. We also identify and compute an $O({e}^{4})$ contribution to $\ensuremath{\Phi}$ coming from vacuum polarization. We discuss the concept of infinite-momentum pathways, the possibility of exponentiation in scalar theories, and speculate on extensions of our work.

Barrier scattering in field theory removal of Klein paradox

The Feynman method of the Green function in quantum electrodynamics is modified to treat scattering problems with a one-dimensional potential. The Green function is constructed from the solutions of the Klein-Gordon (Dirac) equation. The absence of a Klein paradox in a field theoretical treatment is demonstrated. Pair production by the one dimensional potential is considered and the Sauter type potential is used to illustrate general results.