Spinor Quantum Electrodynamics Research Articles

Electron mass anomalous dimension at [formula omitted] in three-dimensional [formula omitted] supersymmetric QED

We consider massless three-dimensional N=1 supersymmetric quantum electrodynamics (QED) with Nf flavours of electrons. Within the dimensional reduction scheme, we compute the critical exponents corresponding to both the electron and selectron field and (parity-even) mass anomalous dimensions at the next-to-leading order in the 1/Nf expansion and in an arbitrary covariant gauge. The equality of the gauge-invariant mass anomalous dimensions of the electron and the selectron is found to result from a subtle role played by the epsilon-scalars. Our general framework also allows us to compute the critical exponents of pure scalar QED and to recover known results in the case of spinor QED. An application of our results to dynamical (s)electron mass generation is considered. We find evidence that, while dynamical flavor symmetry breaking occurs in spinor QED, both pure scalar QED and supersymmetric QED remain in an interacting conformal phase.

N-photon amplitudes in a plane-wave background

We use the worldline formalism to derive master formulas for the one-loop N-photon amplitudes in a plane-wave background, for both scalar and spinor quantum electrodynamics. This generalises previous work by Ilderton and Torgrimsson for the vacuum polarisation case, although with some change in methodology since, instead of evaluating the path integral on the semi-classical trajectory, we use the special kinematics of the plane-wave background to uncover the crypto-gaussian character of this type of worldline path integral.

Unitary versus pseudounitary time evolution and statistical effects in the dynamical Sauter-Schwinger process

Dynamical Sauter-Schwinger mechanism of pair creation by a time-dependent electric field comprising of $N_{\rm rep}$ identical pulses is analyzed within the framework of the spinor and scalar quantum electrodynamics. For linearly polarized pulses, both theories predict that a single eigenmode of the matter wave follows the dynamics of a two-level system. This dynamics, however, is either governed by a Hermitian (for spin 1/2 particles) or pseudo-Hermitian (for spin 0 particles) Hamiltonian. Essentially, both theories lead to a Fraunhofer-type enhancement of the momentum distributions of created pairs. While in the fermionic case the enhancement is never perfect and it deteriorates with increasing the number of pulses in a train $N_{\rm rep}$, in the bosonic case we observe the opposite. More specifically, it is at exceptional points where the spectra of bosonic pairs scale exactly as $N_{\rm rep}^2$, and this scaling is even enhanced with increasing the number of pulses in a train.

All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian.

We provide an explicit expression for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian for both scalar and spinor quantum electrodynamics. To this end, we show that the strong magnetic field behavior is fully determined by one-particle reducible contributions discovered only recently. The latter can efficiently be constructed in an essentially algebraic procedure from lower-order one-particle reducible diagrams. Remarkably, the leading strong magnetic field behavior of the all-loop Heisenberg-Euler effective Lagrangian only requires input from the one-loop Lagrangian. Our result revises previous findings based exclusively on one-particle irreducible contributions. In addition, we briefly discuss the strong electric field limit and comment on external field QED in the large N limit.

Three-loop Euler-Heisenberg Lagrangian in 1+1 QED. Part I. Single fermion-loop part

We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum electrodynamics in 1+1 dimensions. In this first part we calculate the one-fermion-loop contribution, applying both standard Feynman diagrams and the worldline formalism which leads to two different representations in terms of fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the worldline approach allows one to combine the planar and the non-planar contributions to the Lagrangian. Our main interest is in the asymptotic behaviour of the weak-field expansion coefficients of this Lagrangian, for which a non-perturbative prediction has been obtained in previous work using worldline instantons and Borel analysis. We develop algorithms for the calculation of the weak-field expansion coefficients that, in principle, allow their calculation to arbitrary order. Here for the non-planar contribution we make essential use of the polynomial invariants of the dihedral group D4 in Schwinger parameter space to keep the expressions manageable. As expected on general grounds, the coefficients are of the form r1 + r2ζ3 with rational numbers r1, r2. We compute the first two coefficients analytically, and four more by numerical integration.

Worldline sphaleron for thermal Schwinger pair production

With increasing temperatures, Schwinger pair production changes from a quantum tunnelling to a classical, thermal process, determined by a worldline sphaleron. We show this and calculate the corresponding rate of pair production for both spinor and scalar quantum electrodynamics, including the semiclassical prefactor. For electron-positron pair production from a thermal bath of photons and in the presence of an electric field, the rate we derive is faster than both perturbative photon fusion and the zero temperature Schwinger process. We work to all-orders in the coupling and hence our results are also relevant to the pair production of (strongly coupled) magnetic monopoles in heavy ion collisions.

Form factors and related quantities in clothed-particle representation

We show new applications of the notion of clothed particles in quantum field theory. Its realization by means of the clothing procedure put forward by Greenberg and Schweber allows one to express the total Hamiltonian H and other generators of the Poincare group for a given system of interacting fields through the creation (annihilation) operators for the so-called clothed particles with physical (observed) properties. Here such a clothed particle representation is used to calculate the matrix elements (shortly, form factors) of the corresponding Nother current operators sandwiched between the H eigenstates. Our calculations are performed with help of an iterative technique suggested by us earlier when constructing the NN → πNN transition operators. As an illustration, we outline some application of our approach in the spinor quantum electrodynamics.

Strong-field Breit-Wheeler pair production in short laser pulses: Relevance of spin effects

Production of electron-positron pairs in the collision of a high-energy photon with a high-intensity few-cycle laser pulse is studied. By utilizing the frameworks of laser-dressed spinor and scalar quantum electrodynamics, a comparison between the production of pairs of Dirac and Klein-Gordon particles is drawn. Positron energy spectra and angular distributions are presented for various laser parameters. We identify conditions under which predictions from Klein-Gordon theory either closely resemble or largely differ from those of the proper Dirac theory. In particular, we address the question to which extent the relevance of spin effects is influenced by the short duration of the laser pulse.

Semiclassical pair production rate for rotating electric fields

We semiclassically investigate Schwinger pair production for pulsed rotating electric fields depending on time. To do so we solve the Dirac equation for two-component fields in a WKB-like approximation. The result shows that for two-component fields the spin distribution of produced pairs is generally not $1:1$. As a result the pair creation rates of spinor and scalar quantum electro dynamics (QED) are different even for one pair of turning points. For rotating electric fields the pair creation rate is dominated by particles with a specific spin depending on the sense of rotation for a certain range of pulse lengths and frequencies. We present an analytical solution for the momentum spectrum of the constant rotating field. We find interference effects not only in the momentum spectrum but also in the total particle number of rotating electric fields.

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

The Lagrangian formulation of the scalar and spinor quantum electrodynamics in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the “Furry picture” and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the strong-field wave (i.e., the laser) satisfies a massive dispersion relation and obtain self-consistently the effective mass of the laser photons. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.

Fractional effective action at strong electromagnetic fields

In 1936, Weisskopf showed that for vanishing electric or magnetic fields the strong-field behavior of the one loop Euler-Heisenberg effective Lagrangian of quantum electro dynamics (QED) is logarithmic. Here we generalize this result for different limits of the Lorentz invariants \(\vec{E}^2-\vec{B}^2\) and \(\vec{B}\cdot\vec{E}\). The logarithmic dependence can be interpreted as a lowest-order manifestation of an anomalous power behavior of the effective Lagrangian of QED, with critical exponents \(\delta=e^2/(12\pi)\) for spinor QED, and \(\delta_S=\delta/4\) for scalar QED.

Schwinger's pair creation in the combination of a Volkov plane wave and a constant electromagnetic field

We have studied the problem of particle–antiparticle pair creation from vacuum in external fields considering Schwinger's method. The effective action is calculated respectively for scalar and spinor quantum electrodynamics (QED) in the presence of a constant electromagnetic field plus a Volkov plane wave. It is shown that the plane wave has no influence on the process of pair creation.

Photoproduction of Pion Pairs in a Radiation-Dominated Universe. I

Within the framework of scalar quantum electrodynamics (QED) conformally connected with an external gravitational field, the effect of the photoproduction of an arbitrary number of charged massive particle pairs is studied for the quasi-Euclidian model of a radiation-dominated Universe. The total probability of the process is calculated, and the time period during which the given process occurs is determined. The total probability is analyzed and compared with a similar expression obtained in the context of spinor theory. The estimations demonstrate that the total probability of rigid photon decay obtained in the context of scalar theory is by an order of magnitude less than that calculated from the corresponding expression obtained in the context of spinor QED.

Unified radiation formulae for classical and quantum electrodynamics

There are deep conceptual differences between the classical and quantummechanical treatment of electromagnetic radiation processes. Nevertheless, it ispossible to give a formally unified description of the spectral and angulardistribution of radiation in both cases in terms of four-dimensional Fouriertransforms of currents. We present parallel derivations of the basic radiationformulae utilizing classical electrodynamics as well as spinor quantumelectrodynamics. In addition both derivations allow for the presence of amedium with an index of refraction. The practical application of thesemethods is illustrated by calculations of some specific radiation problems.

Lorentz and CPT violations from Chern-Simons modifications of QED

The possibility of a small modification of spinor Quantum Electro-Dynamics is reconsidered, in which Lorentz and CPT non-covariant kinetic terms for photons and fermions are present. The corresponding free field theory is carefully discussed. The finite one-loop parity-odd induced effective action is unambiguously calculated using the physical cutoff method, which manifestly encodes the maximal residual symmetry group allowed by the presence of the Lorentz and CPT breaking axial-vector. This very same induced effective action, which is different from those ones so far quoted in the Literature, is also re-derived by means of the dimensional regularization, provided the maximal residual symmetry is maintained in the enlarged $D$-dimensional space-time. As a consequence, it turns out that the requirement of keeping the maximal residual symmetry at the quantum level just corresponds to the physical renormalization prescription which naturally fixes the one-loop parity-odd induced effective action.

Vacuum polarization in QED with world-line methods

Motivated by several recent papers on string-inspired calculations in quantum electrodynamics (QED), we here present the use of world-line techniques in order to calculate the vacuum polarization and effective action in scalar and spinor QED with an external arbitrary constant electromagnetic field configuration.

On quantum corrections to Chern-Simons spinor electrodynamics

We make a detailed investigation on the quantum corrections to Chern-Simons spinor electrodynamics. Starting from Chern-Simons spinor quantum electrodynamics with the Maxwell term \(-1/(4\gamma){\int}d^3x F_{\mu\nu}F^{\mu\nu}\) and by calculating the vacuum polarization tensor, electron self-energy and on-shell vertex, we explicitly show that the Ward identity is satisfied and hence verify that the physical quantities are independent of the procedure of taking \({\gamma}{\to}{\infty}\) at tree and one-loop levels. In particular, we find the three-dimensional analogue of the Schwinger anomalous magnetic moment term of the electron produced from the quantum corrections.

On quantum corrections to Chern-Simons spinor electrodynamics

We make a detailed investigation on the quantum corrections to Chern-Simons spinor electrodynamics. Starting from Chern-Simons spinor quantum electrodynamics with the Maxwell term $-1/(4\gamma){\int}d^3x F_{\mu\nu}F^{\mu\nu}$ and by calculating the vacuum polarization tensor, electron self-energy and on-shell vertex, we explicitly show that the Ward identity is satisfied and hence verify that the physical quantities are independent of the procedure of taking ${\gamma}{\to}{\infty}$ at one-loop and tree levels. In particular, we find the three-dimensional analogue of the Schwinger anomalous magnetic moment term of the electron produced from the quantum corrections.

Topological unitarity identities in Chern-Simons theories.

Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of Feynman diagrams with a given number of internal on-shell free topological photon lines. It is also shown, that these identities can be derived outside the framework of perturbation theory. The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order.

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.