Broken supersymmetry and the divergence of the perturbation series in QED

The n-bubble diagram contributions to the electron anomalous magnetic moment are studied. In supersymmetric QED, the photon- and photino-exchange contributions exactly cancel. When supersymmetry is broken, n! growth is restored and Borel summability is apparently lost. The potential first renormalon singularity is absent but the second is present in both the non-supersymmetric and broken supersymmetry cases. Other possibilities for Borel summability are discussed.     

Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients

We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating series superior to those obtained using Pade approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Pade method.     

Quantum instability in cavity QED

The stability and instability of quantum evolution are analyzed in the interaction of a two-level atom with a quantized-field mode in an ideal cavity with allowance for photon recoil, which is the basic model of cavity QED. It is shown that the Jaynes-Cammings quantum dynamics can be unstable in the regime of the random walk of the atom in the quantized field of a standing wave in the absence of any interaction with the environment. This instability is manifested in large fluctuations of the quantum entropy, which correlate with a classical-chaos measure, the maximum Lyapunov exponent, and in the exponential sensitivity of the fidelity of the quantum states of the strongly coupled atom-field system to small variations of resonance detuning. Numerical experiments reveal the sensitivity of the atomic population inversion to the initial conditions and to correlation between the quantum and classical degrees of freedom of the atom.     

The infinite coupling limit and the asymptotics of coefficients of the perturbation expansion

For some functions in quantum field theory and quantum mechanics, presented by the asymptotic expansion in coupling constant g, the method for finding the approximate asymptotics when g is proposed.Such an estimation requires the first exact terms of the perturbation theory, their high-order asymptotics and supposition on the Borel summability. This method for the Gell-Mann-Low function (g) in the (4²/3)g ₍₄₎ ⁴ model gives approximately (g) 1.8 g ².     

A convergent series for the QED effective action

The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one-loop effective action of QED.     

Vacuum copies and perturbation theory in the 't hooft-veltman gauge of QED

The 't Hooft-Veltman gauge condition ?_μA_μ + A_μ² = 0 gives a version of quantum electrodynamics with many similarities to Yang-Mills theory, including the presence of Gribov gauge-fixing ambiguities. We exhibit and discuss some properties of a family of copies of the vacuum, emphasizing their bearing on perturbation theory and the choice of a vacuum state. It is shown that in a general gauge theory, the same perturbation series results from expanding about any gauge-copy of the vacuum.     

Noncommutative cumulants for stochastic differential equations and for generalized Dyson series

For the stochastic equationU=VU, Kubo's ansalze for U in the form of differential and integrodifferential equations is investigated and a newansatz as an integral equation is added. Unique solutions in terms of noncommutative W- and K-cumulants are found by elementary functional differentiation, and expressions of van Kämpen and Terwiel are recovered. For the cumulants we find simple recursion relations and prove the important cluster property. Surprisingly, it is found that the Gaussian approximation in the differential equationansatz leads to positivity problems, while this is not the case with the integral and integrodifferential equation. The cumulant expansion technique is carried over to generalized Dyson series. In a companion paper we apply our results to quantum shot noise.     

Observing quantum tunneling in perturbation series

We apply Borel resummation to the conventional perturbation series of ground state energy in a metastable potential, V(x) = x²/2 − gx⁴/4. We observe numerically that the discontinuity of the Borel transform reproduces the imaginary part of the energy eigenvalue, i.e., the total decay width due to quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling regime 0 < g 0.7.     

High-amplitude single-mode perturbation evolution at the Richtmyer-Meshkov instability

The single-mode Richtmyer-Meshkov hydrodynamic instability at light/heavy (air/SF6 and air/CO2), close density (air/N2), and heavy/light (air/He) interfaces has been experimentally studied for a low incident shock wave Mach number. Two identical 2D half sinusoidal initial perturbations, with a relatively high initial amplitude, were considered in order to rapidly reach the nonlinear regime and check the reduction of the initial growth rate compared to that predicted by the small-amplitude theory. The growth rate measurements for the air/SF6 and air/CO2 cases are in excellent agreement with the nonlinear model of Sadot et al. coupled with a reduction factor suggested by Rikanati et al. In the air/N2 case, the reversal phase can be precisely described by the linear theory. Finally, the heavy/light experiment is well described by the Vandenboomgaerde model also coupled with a smaller reduction factor.     

Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime

A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of . We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution and day-night asymmetry of events due to Lorentz violation and the earth's rotation will be useful in identifying signals. We also comment briefly on the high energy behavior of the cross section that grows linearly in the center of mass energy squared and argue that it does not necessarily contradict some statements, e.g., the Froissart-Martin bound, achieved in ordinary theory. Received: 29 November 2002 / Revised version: 11 March 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: liaoy@itp.uni-leipzig.de RID="b" ID="b" e-mail: dehne@itp.uni-leipzig.de     

Summation of perturbation series in the generalized Hubbard model

The cumulant expansion is proposed for the summation of perturbation series in the generalized Hubbard model, which considers strongly correlated d-electrons hybridized with nearly free conduction electrons. It is shown, that summation of the principle series for the Green's functions leads to the Kondo renormalization of d-level hybridized with s-band.     

Summing up the perturbation series in the Schwinger Model

Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation, performed entirely in momentum space, shows the complete agreement between nonperturbative and perturbative approaches. Received: 2 March 1998 / Revised version: 12 May 1998 / Published online: 8 September 1998     

On the perturbation series for radiative effects

We present a generalization of the recently developed first-order perturbation approximation for the computation of radiative effects such as layer heating rates and surface fluxes. The basis for this generalization is Dyson's equation for Green's function or the inverse transport operation.     

The instability analysis of self-gravitation systems under the perturbation with orbital angular momentum

Based on plasma kinetic theory, the instabilities of self-gravitation systems under perturbation with orbital angular momentum(OAM) are investigated, and the concept of twisted Jeans mode is introduced to describe the new phenomenon. The result shows that the growth rate of the Jeans instability is enhanced with the OAM parameter increased, while the critical wave number is consistent with the classical Jeans critical value. It is expected that the present results would give more insight into th...     

On the summation of the Brillouin-Wigner type perturbation series

It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.     

A method for summation of perturbation series

A method for summation of perturbation series is developed. It consists of a proper rearrangement of the power series through an appropriate redefinition of the perturbation parameter. Well-known divergent power series appearing in a φ⁴-scalar field theory or in the treatment of the linear confining potential model and the Stark effect in hydrogen are used as illustrative examples. A comparison between present results and accurate, numerical ones shows that our series converge even faster than sequences of Padé or Borel-Padé approximants.