Field asymptotic behavior of a polarization operator

Loskutov, Yu. M.; Lysov, B.A.; Скобелев, В. В.

doi:10.1007/bf01027806

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“…As in the 4D case, we shall assume that spin does not play a role in this limit, so that (1.28) holds for spinor QED unchanged (let us also mention here that Loskutov et al [42] have found an all-loop exponentiation formula similar to (1.28) for the strong-field asymptotics of the electron mass operator in a two-dimensional approximation of four-dimensional QED).…”

Section: Number Of External Legsmentioning

confidence: 99%

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED. Part I: two-loop

Huet

McKeon

Schubert

2010

J. High Energ. Phys.

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We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l -loop N -photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this 'Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.

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Section: Number Of External Legsmentioning

confidence: 99%