Massless Quantum Electrodynamics Research Articles

Beyond N = ∞ in large N conformal vector models at finite temperature

We investigate finite-temperature observables in three-dimensional large N critical vector models taking into account the effects suppressed by 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document}. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar O(N) model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document}, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite N, while in special cases the discrepancies only start to appear at the next-to-subleading order.

Noninvertible Chiral Symmetry and Exponential Hierarchies

We elucidate the fate of classical symmetries which suffer from Abelian Adler-Bell-Jackiw anomalies. Instead of being completely destroyed, these symmetries survive as noninvertible topological global symmetry defects with world volume anyon degrees of freedom that couple to the bulk through a magnetic 1-form global symmetry as in the fractional Hall effect. These noninvertible chiral symmetries imply selection rules on correlation functions and arise in familiar models of massless quantum electrodynamics and models of axions (as well as their non-Abelian generalizations). When the associated bulk magnetic 1-form symmetry is broken by the propagation of dynamical magnetic monopoles, the selection rules of the noninvertible chiral symmetry defects are violated nonperturbatively. This leads to technically natural exponential hierarchies in axion potentials and fermion masses.Received 3 August 2022Accepted 2 February 2023DOI:https://doi.org/10.1103/PhysRevX.13.011034Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnomaliesPhysical SystemsAxionsPropertiesChiral symmetryTechniquesMonopolesParticles & Fields

The quantum scale invariance in graphene-like quantum electrodynamics

The ultraviolet and infrared finiteness of a parity-even massless planar quantum electrodynamics mimics the scale invariance in graphene.

Infrared finite scattering theory in quantum field theory and quantum gravity

It has been known since the earliest days of quantum field theory (QFT) that infrared divergences arise in scattering theory with massless fields. These infrared divergences are manifestations of the memory effect: At order $1/r$ a massless field generically will not return to the same value at late retarded times ($u\ensuremath{\rightarrow}+\ensuremath{\infty}$) as it had at early retarded times ($u\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$). There is nothing singular about states with memory, but they do not lie in the standard Fock space. Infrared divergences are merely artifacts of trying to represent states with memory in the standard Fock space. If one is interested only in quantities directly relevant to collider physics, infrared divergences can be successfully dealt with by imposing an infrared cutoff, calculating inclusive quantities, and then removing the cutoff. However, this approach does not allow one to treat memory as a quantum observable and is highly unsatisfactory if one wishes to view the $S$-matrix as a fundamental quantity in QFT and quantum gravity, since the $S$-matrix itself is undefined. In order to have a well-defined $S$-matrix, it is necessary to define ``in'' and ``out'' Hilbert spaces that incorporate memory in a satisfactory way. Such a construction was given by Faddeev and Kulish for quantum electrodynamics (QED) with a massive charged field. Their construction can be understood as pairing momentum eigenstates of the charged particles with corresponding memory representations of the electromagnetic field to produce states of vanishing large gauge charges at spatial infinity. (This procedure is usually referred to as ``dressing'' the charged particles.) We investigate this procedure for QED with massless charged particles and show that, as a consequence of collinear divergences, the required dressing in this case has an infinite total energy flux, so that the states obtained in the Faddeev-Kulish construction are unphysical. An additional difficulty arises in Yang-Mills theory, due to the fact that the ``soft Yang-Mills particles'' used for the dressing contribute to the Yang-Mills charge-current flux, thereby invalidating the procedure used to construct eigenstates of large gauge charges at spatial infinity. We show that there are insufficiently many charge eigenstates to accommodate scattering theory. In quantum gravity, the analog of the Faddeev-Kulish construction would attempt to produce a Hilbert space of eigenstates of supertranslation charges at spatial infinity. Again, the Faddeev-Kulish dressing procedure does not produce the desired eigenstates because the dressing contributes to the null memory flux. We prove that there are no eigenstates of supertranslation charges at spatial infinity apart from the vacuum. Thus, analogs of the Faddeev-Kulish construction fail catastrophically in quantum gravity. We investigate some alternatives to Faddeev-Kulish constructions but find that these also do not work. We believe that if one wishes to treat scattering at a fundamental level in quantum gravity---as well as in massless QED and Yang-Mills theory---it is necessary to approach it from an algebraic viewpoint on the ``in'' and ``out'' states, wherein one does not attempt to ``shoehorn'' these states into some prechosen ``in'' and ``out'' Hilbert spaces. We outline the framework of such a scattering theory, which would be manifestly infrared finite.

Electron mass singularities in semileptonic kaon decays

We show that recent improvements in the $O(\alpha)$ long-distance quantum electrodynamics (QED) corrections to the radiative inclusive $K_{e3}$ decay rate using the Sirlin representation are free from infrared divergences and collinear electron mass singularities in the limit $m_e\rightarrow0$, as predicted by the Kinoshita-Lee-Nauenberg theorem. We also verify that in massless QED with the simultaneous dimensional regularization of QED photon infrared divergences and electron mass singularities leads to the same result for the inclusive rate in the limit of four space-time dimensions. The equivalence of the two approaches results in part from an interesting interplay between a small chirality-breaking effect in the massless electron limit and the generalization of space-time algebra and phase space integrals to $d>4$ dimensions. Our finding supports the small theoretical uncertainty claimed for $K_{e3}$ radiative inclusive rates and reaffirms its utility in precision unitarity tests of the quark mixing matrix.

Real time ultrasoft fermion self energy at next to-leading order in hot QED

Subsequent studies of the behavior of the gluon and quark damping rates in the imaginary-time formalism have indicated that there are difficulties in the infrared sector [1, 2, 3, 4, 5, 6, 7]. To look further into the infrared behavior, we propose to calculate the next-to-leading order dispersion relations for slow-moving Fermions at high-temperature quantum electrodynamics (QED) in real-time formalism. We determine a compact analytic expression for the complete next-to-leading contribution to the retarded fermion self-energy with ultrasoft momentum in the framework of hard-thermal-loop (HTL)-summed perturbation of massless QED at high temperature. The calculation is done using real-time formalism. The next-to-leading order fermion self-energy is written in terms of three and four HTL-dressed vertex functions. The real part and the opposite of the imaginary part of the retarded fermion self-energy are related to the next-to-leading order contributions of energy and damping rate respectively.

On the creation of charged massless fermion pair by a photon in an external constant uniform magnetic field in 2+1 dimensions

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the [Formula: see text]-dimensional quantum electrodynamics (QED[Formula: see text]). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

Anisotropic fixed points in Dirac and Weyl semimetals

The effective low energy description of interacting Dirac and Weyl semimetals is that of massless quantum electrodynamics with several Lorentz breaking material parameters. We perform a renormalization group analysis of Coulomb interaction in anisotropic Dirac and Weyl semimetals and show that the anisotropy persists in the material systems at the infrared fixed point. In addition, a tilt of the fermion cones breaking inversion symmetry induces a magnetoelectric term in the electrodynamics of the material whose magnitude runs to match that of the electronic tilt at the fixed point.

Note on soft photons and Faddeev–Jackiw symplectic reduction of quantum electrodynamics in the eikonal limit

In this note, we go over the recent soft photon model and Faddeev–Jackiw quantization of the massless quantum electrodynamics in the eikonal limit to some extent. Throughout our readdressing, we observe that the gauge potentials in both approaches become pure gauges and the associated eikonal Faddeev–Jackiw quantum bracket matches with the soft quantum bracket. These observations and the fact that the gauge fields in two cases localize in two-dimensional plane (even if it is spatial in soft photon case and (1[Formula: see text]+[Formula: see text]1)-dimensional Minkowski in the eikonal case) imply that there might be an interesting relation between these two distinct perspectives.

Generalized Dirac structure beyond the linear regime in graphene

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third-order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analog massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena.

Spontaneous breaking of Lorentz symmetry in ( 2+ε )-dimensional QED

The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < N_c^{\chi SB}$ the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using $\epsilon$ expansion near the lower critical dimension of 2, as well as the recent results on the generalization of the $F$ theorem to continuous dimension, we show that $N_c^{conf} > N_c^{\chi SB}$. There is therefore an intermediate range of values of $N$ at which a third phase is stabilized. We demonstrate that this phase is characterized by spontaneous breaking of Lorentz symmetry, in which a composite vector boson field acquires a vacuum expectation value with the fermions and the photon remaining massless.

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3**Supported by the Natural Science Foundation of Jiangsu Province under Grant No BK20130387, and the Fundamental Research Funds for the Central Universities under Grant No 2242014R30011.

Since the massless quantum electrodynamics in 2+1 dimensions (QED3) with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζc. Based on the feature of chiral susceptibility, we show that the system at ζc exhibits a second-order phase transition which accords with the nature of appearance of the high-Tc superconductivity, and the estimated critical exponents around ζc are illustrated.

Lorentz contraction of the equal-time Bethe–Salpeter amplitude in two-dimensional massless quantum electrodynamics

The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so called Schwinger Model) are considered. It is shown that while boosting a bound state (a `meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles (`quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full} function, i.e. with the inclusion of all instanton contributions has to be considered. The amplitude in each separate topological sector does not exhibit such properties.

Time-dependent pair creation and the Schwinger mechanism in graphene

The momentum spectrum of positively and negatively charged carriers created in intrinsic graphene submitted to a time-dependent external electric field is evaluated for many external field configurations. Owing to the formal analogy between relativistic quantum mechanics and the description of graphene quasiparticles in terms of the massless Dirac equation, the electron momentum density is evaluated within two-dimensional massless quantum electrodynamics coupled to a strong classical field. This allows the treatment of dynamical effects in electron-hole creation and gives a physical description in terms of the time-dependent Schwinger mechanism. At zero transverse momentum, it is shown that the Fermi bound in the electron-hole momentum spectrum is saturated in a certain momentum window and the pair density depends only on the potential difference between asymptotic potentials before and after the interaction. The pair density for nonzero transverse momenta is evaluated using numerical calculations. The numerical results demonstrate that an important number of pairs can be created by an external field through both tunneling and multiphoton processes. It is argued that these features of the dynamical pair production may facilitate the detection of the Schwinger mechanism using graphene as a condensed matter analog to quantum electrodynamics.

Synchrotron radiation from massless charge

Classical radiation power from an accelerated massive charge diverges in the zero-mass limit, while some authors suggest that strictly massless charge does not radiate at all. On the other hand, the regularized classical radiation reaction force, though looking odd, is non-zero and finite. To clarify this controversy, we consider radiation problem in massless scalar quantum electrodynamics in the external magnetic field. In this framework, synchrotron radiation is found to be non-zero, finite, and essentially quantum. Its spectral distribution is calculated using Schwinger's proper time technique for ab initio massless particle of zero spin. Provided E2≫eH, the maximum in the spectrum is shown to be at ħω=E/3, and the average photon energy is 4E/9. The normalized spectrum is universal, depending neither on E nor on H. Quantum nature of radiation makes classical radiation reaction equation meaningless for massless charge. Classical theory is reliable only as providing the low-frequency part of the true quantum radiation spectrum.

Gravitational corrections to the scattering in a massless quantum electrodynamics

We discuss the role of gravitational corrections to the running of the electric charge through the evaluation of scattering amplitudes of charged particles in massless scalar electrodynamics. Computing the complete divergent part of the $S$-matrix amplitude for two distinct scattering processes, we show that quantum gravitational corrections do not alter the running behavior of the electric charge. Our result does not exclude the possibility that the presence of a second dimensional constant in the model (a cosmological constant or the presence of massive particles) could alter this behavior, as was proposed in earlier works.

Electrodynamics modified by some dimension-five Lorentz-violating interactions: radiative corrections

We study radiative corrections to massless quantum electrodynamics modified by two dimension-five LV interactions $\bar{\Psi} \gamma^{\mu} b'^{\nu} F_{\mu\nu}\Psi$ and $\bar{\Psi}\gamma^{\mu}b^{\nu} \tilde{F}_{\mu\nu} \Psi$ in the framework of effective field theories. All divergent one-particle-irreducible Feynman diagrams are calculated at one-loop order and several related issues are discussed. It is found that massless quantum electrodynamics modified by the interaction $\bar{\Psi} \gamma^{\mu} b'^{\nu} F_{\mu\nu}\Psi$ alone is one-loop renormalizable and the result can be understood on the grounds of symmetry. In this context the one-loop Lorentz-violating beta function is derived and the corresponding running coefficients are obtained.

Avoidance of a Landau pole by flat contributions in QED

We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons.

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.