Massless Quantum Electrodynamics Research Articles

Consistency of loop regularization method and divergence structure of QFTs Beyond one-loop order

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.

Massless fermions in multiflavorQED2

The ground state of the multiflavor two-dimensional quantum electrodynamics is determined in the presence of finite baryon density, and it is shown that the model possesses two phases: the low-density phase where the external baryon density is totally screened, and the high-density phase where the screening is only partial. The renormalization of the bosonized version of the model is also performed for both the zero and the finite-density model giving massless multiflavor two-dimensional quantum electrodynamics in both cases.

THE EFFECTIVE POTENTIAL IN THE MASSIVE $\phi_4^4$ MODEL

By applying the renormalization group equation, it has been shown that the effective potential V in the massless [Formula: see text] model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive [Formula: see text] model, showing that the effective potential is independent of ϕ here as well.

THE BEHAVIOR OF THE GAUGE-BOSON PROPAGATOR IN THE DIFFERENT PHASES OF QED3

As a toy model of quantum chromodynamics (QCD), we investigate the influence of the vacuum polarization on the photon propagator, in massless quantum electrodynamics in 2+1 dimensions (QED3), using the coupled Dyson–Schwinger equations for the fermion and photon propagators with a range of fermion–photon vertices. It is found that the form of the photon propagators in the Nambu–Goldstone and Wigner phases exhibit distinctly different behaviors and it is expected that similar things happen in QCD. Hence in the phenomenological application of QCD one should choose different forms of gluon propagator as input to solve the quark self-energy functions in the two different phases, especially in the study of QCD phase transitions. In addition, employing these results, we discuss the causation of dynamical chiral symmetry breaking (DCSB) in QED3 and compare it with that in QCD.

MASSLESS THREE-DIMENSIONAL QUANTUM ELECTRODYNAMICS AND THIRRING MODEL CONSTRAINED BY LARGE FLAVOR NUMBER

We explicitly prove that in three-dimensional massless quantum electrodynamics at finite temperature, zero density and large number of flavors, the number of infrared degrees of freedom is never larger than the corresponding number of ultraviolet. Such a result, strongly dependent on the asymptotic freedom of the theory, is reversed in three-dimensional Thirring model due to the positive derivative of its running coupling constant.

Renormalization of QED with planar binary trees

The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.

Gauge independence of the limiting cases of the one-loop electron dispersion relation in high-temperature QED

Assuming high temperature and taking subleading temperature dependence into account, the gauge dependence of one-loop electron dispersion relation is investigated in massless quantum electrodynamics (QED) at zero chemical potential. The analysis is carried out using a general linear covariant gauge. The equation governing the gauge dependence of the dispersion relation is obtained and used to prove that the dispersion relation is gauge independent in the limiting case of momenta much larger than $\mathrm{eT}.$ It is also shown that the effective mass is not influenced by the leading temperature dependence of the gauge dependent part of the effective self-energy. As a result, the effective mass, which is of order $eT,$ does not receive a correction of order ${e}^{2}T$ from one-loop, independent of the gauge parameter.

A nonunitary version of massless quantum electrodynamics possessing a critical point

Recently, it has been observed that a quantum field theory need not be hermitian to have a real, positive spectrum. What seems to be required is symmetry under combined parity and time-reversal transformations. This idea is extended to massless electrodynamics, in which the photon couples to the axial-vector current with an imaginary coupling constant. The eigenvalue condition necessary for the finiteness of the theory can now be solved; the value for the charge appears to be stable order-by-order. Similarly, the semiclassical Casimir model for the fine-structure constant yields a positive value.

Analysis of the chiral anomaly in dimensional regularization by the projection technique

A self-consistent method for calculating the chiral anomaly in dimensional regularization without the four-dimensional symbols γ5 and ɛμνλρ is proposed. The method is applied to the calculation and analysis of chiral symmetry in massless quantum electrodynamics.

Free energy of high temperature QED to order e5 from effective field theory.

Massless quantum electrodynamics is studied at high temperature and zero chemical potential. We compute the Debye screening mass to order $e^{4}$ and the free energy to order $e^{5}$} by an effective field theory approach, recently developed by Braaten and Nieto. Our results are in agreement with calculations done in resummed perturbation theory. This method makes it possible to separate contributions to the free energy from different momentum scales (order $T$ and $eT$) and provides an economical alternative to computations in the full theory which involves the dressing of internal propagators.

Screening of static electromagnetic fields in hot QED plasmas.

We study the screening of static magnetic and electric fields in massless quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at temperature $T$. Various exact relations for the static polarisation tensor are first reviewed and then verified perturbatively to fifth order (in the coupling) in QED and fourth order in SQED, using different resummation techniques. The magnetic and electric screening masses squared, as defined through the pole of the static propagators, are also calculated to fifth order in QED and fourth order in SQED, and their gauge-independence and renormalisation-group invariance is checked. Finally, we provide arguments for the vanishing of the magnetic mass to all orders in perturbation theory.

Three-loop equation of state of QED at high temperature.

We present the three loop contribution (order $e^4$) to the pressure of massless quantum electrodynamics at nonzero temperature. The calculation is performed within the imaginary time formalism. Dimensional regularization is used to handle the usual, intermediate stage, ultraviolet and infrared singularities, and also to prevent overcounting of diagrams during resummation.

The free energy of hot QED at fifth order

The order e 5 contribution to the pressure of massless quantum electrodynamics at nonzero temperature is determined explicitly. An identity is also obtained relating a gauge-invariant piece of the pressure at order e 2 n+3 ( n ⩾ 1) (from diagrams with only one fermion loop) to the pressure at order e 2 n . Prospects for higher order calculations are discussed and potential applications are mentioned.

THE CLASSICAL ELECTROMAGNETIC THEORY CORRESPONDING TO THE MASSLESS TWO-DIMENSIONAL SPINOR QUANTUM ELECTRODYNAMICS

We analyze the physical meaning of the classical electromagnetic theory underlying the massless two-dimensional spinor quantum electrodynamics (Schwinger model) and show that the vector and axial vector currents are dually equivalent. The resulting dual classical electromagnetic theory is shown to be consistent.

Gauge covariance and the fermion-photon vertex in three- and four-dimensional, massless quantum electrodynamics.

In the quenched approximation, the gauge covariance properties of three vertex Ans\"{a}tze in the Schwinger-Dyson equation for the fermion self energy are analysed in three- and four- dimensional quantum electrodynamics. Based on the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the spectral representation used for the vertex in the gauge technique cannot support dynamical chiral symmetry breaking. A criterion for establishing whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson equation is presented and the Curtis and Pennington Ansatz is shown to satisfy this constraint. We obtain an analytic solution of the Schwinger-Dyson equation for quenched, massless three-dimensional quantum electrodynamics for arbitrary values of the gauge parameter in the absence of dynamical chiral symmetry breaking.

Free and interacting 2D Maxwell field theory on conformally flat spacetimes

This paper concerns the quantization of massless quantum electrodynamics on a general two-dimensional Riemannian manifold (QED2). The central result is the derivation of the propagators and vertex correlation functions at the lowest order on any closed and orientable Riemann surface. This also allows the perturbative treatment of QED2 in the case of non-trivially curved spacetimes and the explicit calculation of the physical observables at any order. Moreover, the perturbative approach described in this paper can also be applied to string theories. To this purpose, two models are presented describing possible interactions between Abelian gauge fields and string theory.

Asymptotic fermion propagator in massless three-dimensional QED.

Massless quantum electrodynamics in two spatial and one time dimensions has a logarithmically confining static Coulomb potential, and thus nontrivial infrared behavior. We apply a technique developed for ordinary four-dimensional quantum electrodynamics in which the charged asymptotic states in the theory are dressed with soft vector bosons, in order to improve the representation of the infrared dynamics in perturbation theory. The resulting modification to the mass-shell behavior of the fermion propagator is determined, with the result that the propagator no longer possesses a mass-shell singularity.

A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to Two-Loop Order

We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all 1- and 2-loop 1PI diagrams, run renormalization group equations on them and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle $\gamma_5$ problems.

Delta expansion for local gauge theories. II. Nonperturbative calculation of the anomaly in the Schwinger model.

This is the second paper in a series in which we show how to use the principles of the $\ensuremath{\delta}$ expansion to obtain nonperturbative solutions to gauge theories. The approach consists of replacing the usual minimal-coupling term $\overline{\ensuremath{\psi}}(\ensuremath{\partial}\ensuremath{-}eA)\ensuremath{\psi}$ by $\overline{\ensuremath{\psi}}{(i\ensuremath{\partial}\ensuremath{-}eA)}^{\ensuremath{\delta}}\ensuremath{\psi}$ and then expanding the new theory in powers of $\ensuremath{\delta}$. For all values of $\ensuremath{\delta}$ the theory is locally gauge invariant. Thus, local gauge invariance holds order by order in powers of $\ensuremath{\delta}$. In this paper we show how to calculate the photon propagator and thus the anomaly in the Schwinger model (two-dimensional massless quantum electrodynamics) to first order in $\ensuremath{\delta}$. At $\ensuremath{\delta}=1$ the exact value for the anomaly, $\frac{{e}^{2}}{\ensuremath{\pi}}$, is obtained.

GAUGE INVARIANT STUDY OF THE STRONG COUPLING PHASE OF MASSLESS QUANTUM ELECTRODYNAMICS

The strong coupling phase of massless Quantum Electrodynamics is studied in a gauge invariant way. The formalism is given in which the order parameter of the chiral symmetry breaking is calculated through the vacuum polarization diagrams. Applying this method, the critical coupling constant is shown to exist that is independent of the gauge parameter but is now dependent on the ratio of the two kinds of cutoff. Implication of this new parameter on the renormalization scheme in the strong coupling phase is discussed.