Quenched Quantum Electrodynamics Research Articles

Quantum electrodynamics on the lattice and numerical perturbative computation of g − 2

Abstract We compute the electron g factor to the $\mathcal {O}(\alpha ^5)$ order on the lattice in quenched quantum electrodynamics (QED). We first study finite volume (FV) corrections in various infrared regularization methods to discuss which regularization is optimal for our purpose. We find that in QEDL the FV correction to the effective mass can have different parametric dependences depending on the size of Euclidean time t and match the ‘naive on-shell result’ only at the very large t region, t ≫ L. We adopt finite photon mass regularization to suppress FV effects exponentially and also discuss our strategy for selecting simulation parameters and the order of extrapolations to efficiently obtain the g factor. We perform lattice simulation using small lattices to test the feasibility of our calculation strategy. This study can be regarded as an intermediate step toward giving the five-loop coefficient independently of preceding studies.

Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.

Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

We study the gauge-covariance of the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit \ep \to 0, we state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.

Dynamical mass generation in QED with magnetic fields: Arbitrary field strength and coupling constant

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetics fields of arbitrary strength, by solving the Schwinger-Dyson equation for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass $m$ for arbitrarily small values of electromagnetic coupling $\ensuremath{\alpha}$. For intense fields it is also well known that $m\ensuremath{\propto}\sqrt{eB}$. Our approach allows us to span all regimes of parameters $\ensuremath{\alpha}$ and $eB$. We find that $m\ensuremath{\propto}\sqrt{eB}$ provided $\ensuremath{\alpha}$ is small. However, when $\ensuremath{\alpha}$ increases beyond the critical value ${\ensuremath{\alpha}}_{c}$ which marks the onslaught of dynamical fermion masses in vacuum, we find $m\ensuremath{\propto}\ensuremath{\Lambda}$, the cutoff required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of $eB$ and $\ensuremath{\alpha}$. We also point out the relevance of our work for possible physical applications.

Dynamical mass generation in strongly coupled quantum electrodynamics with weak magnetic fields

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of weak magnetic fields using Schwinger-Dyson equations. Contrary to the case where the magnetic field is strong, in the weak field limit the coupling should exceed certain critical value in order for the generation of masses to take place, just as in the case where no magnetic field is present. The weak field limit is defined as eB<<m(0){sup 2}, where m(0) is the value of the dynamically generated mass in the absence of the field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB){sup 2}.

On the two-point Green function in QED

It is well known how multiplicative renormalizability of the fermion propagator results in a simple form of the corresponding Schwinger-Dyson equation in the momentum space in massless quenched quantum electrodynamics in 4-dimensions (QED4). We extend this idea to arbitrary dimensions d. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in d-dimensions

Numerical study of dynamical mass generation in QED3

We carry out a numerical study of dynamical generation of fermion masses by solving the Schwinger-Dyson equation for the fermion propagator in three-dimensional quenched Quantum Electrodynamics (QED3) in various gauges. We employ an ansatz for the three-point vertex which satisfies the Ward-Green-Takahashi identity, namely, the Ball-Chiu Vertex. We discuss the advantages of our numerical method over some earlier ones.

Dynamical fermion masses and constraints of gauge invariance in quenched QED3

Numerical study of the Schwinger–Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge ξ is a complicated exercise specially if one employs a sophisticated form of the fermion–boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger–Dyson equation for every value of ξ. In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau–Khalatnikov–Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of ξ. We also compare our results with exact numerical solutions available for a small number of values of ξ obtained through a direct analysis of the corresponding SDE.

The nonperturbative propagator and vertex in massless quenched QEDd

It is well known how multiplicative renormalizability of the fermion propagator, through its Schwinger-Dyson equation, imposes restrictions on the 3-point fermion-boson vertex in massless quenched quantum electrodynamics in 4-dimensions (QED$_4$). Moreover, perturbation theory serves as an excellent guide for possible nonperturbative constructions of Green functions. We extend these ideas to arbitrary dimensions $d$. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in $d$-dimensions and it naturally leads to a constraint on the fermion-boson vertex. We verify that this constraint is satisfied in perturbation theory at the one loop level in 3-dimensions. Based upon one loop perturbative calculation of the vertex, we find additional restrictions on its possible nonperturbative forms in arbitrary dimensions.

Dynamical mass generation for fermions in quenched quantum electrodynamics at finite temperature

We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics (QQED) at finite temperature in the bare vertex approximation, using Schwinger-Dyson equations (SDE's). Motivated by perturbation theory, a further simplification is introduced by taking the wave function renormalization to be unity. In the zeroth mode approximation, the SDE for the fermion propagator resembles QED in 2+1 dimensions $({\mathrm{QED}}_{3})$ at zero temperature with an effective dimensionful coupling ${\ensuremath{\alpha}}^{\ensuremath{'}}=\ensuremath{\alpha}T.$ For a fixed temperature, the mass is dynamically generated above a certain critical value of this coupling. As expected, raising the temperature restores chiral symmetry and fermions become massless again. We also argue that by summing over the frequency modes and under suitable simplifications, qualitative aspects of the result do not undergo significant changes.

Gauge dependence of mass and condensate in chirally asymmetric phase of quenched three-dimensional QED

We study three dimensional quenched Quantum Electrodynamics in the bare vertex approximation. We investigate the gauge dependence of the dynamically generated Euclidean mass of the fermion and the chiral condensate for a wide range of values of the covariant gauge parameter $\xi$. We find that (i) away from $\xi=0$, gauge dependence of the said quantities is considerably reduced without resorting to sophisticated vertex {\em ansatze}, (ii) wavefunction renormalization plays an important role in restoring gauge invariance and (iii) the Ward-Green-Takahashi identity seems to increase the gauge dependence when used in conjunction with some simplifying assumptions. In the Landau gauge, we also verify that our results are in agreement with those based upon dimensional regularization scheme within the numerical accuracy available.

An integral equation of Muskhelishvili type: Strong quantum electrodynamics

An equation that arises out of the bifurcation analysis of an improvement of the nonperturbative equations for the electron mass function in quenched quantum electrodynamics is analyzed. In the quasilinear approximation, the integral equation is solved by Mellin transformation, followed by the calculation of the Muskhelishvili index of the resultant singular integral operator.

Non-mean-field exponents in strongly coupled quenched QED.

We study quenched quantum electrodynamics (QED) on a lattice in the noncompact formulation. Near the chiral critical point, we avoid critical slowing down using fast-Fourier-transform methods which allow us to obtain critical indices with good accuracy. Using lattices of 16{sup 4} and 24{sup 4} sites and masses between 0.025 and 0.0007 (lattice units) we found that the critical behavior of QED is described by power laws with critical exponents differing from mean-field results. The critical coupling is {beta}{sub {ital c}}=0.257{plus minus}0.001, the exponent {delta} is 2.2{plus minus}0.1, and the magnetic exponent {beta}{sub {ital m}} is 0.78{plus minus}0.08. A physical explanation of our results is presented.

Scaling properties of quenched QED.

Critical scaling laws are studied in quenched quantum electrodynamics with induced four-fermion interactions that drive the theory to criticality. The critical exponents are calculated in the quenched, planar model and the physical picture extracted is consistent with recent results from lattice simulations. Near criticality, a composite scalar state plays an essential role in the effective dynamics.

Strongly coupled quenched QED

We consider quenched quantum electrodynamics at strong coupling as an ultra-violet stable fixed point field theory. We discuss the collapse of the wave function phenomenon of the Dirac equation and its relation to chiral symmetry breaking and the formation of a condensate. The scaling laws of 〈 ΨΨ〉 are obtained in the strongly coupled phase and near the critical point using Schwinger-Dyson equations. We formulate the non-compact theory on the lattice and study the scaling laws of 〈 ΨΨ〉 numerically. The spectrum of the model is studied by computer simulation methods and we estimate the masses of the pion, sigma, rho and A 1.

On the existence of quantum electrodynamics.

We explain from an intuitive renormalization-group perspective how "collapse of the wave function" in quenched quantum electrodynamics leads to coupling-constant renormalization and an interacting ultraviolet stable fixed point. A diagrammatic expansion in ${N}_{f}$, the number of fermion species, suggests that vacuum polarization leads the fixed point of the quenched model stable, and computer-simulation data support this possibility. The scaling region of the quenched lattice model is discovered numerically.