QED effective action revisited

Gies, Holger; Valluri, S. R.; Lamm, D. R.; Weniger, Ernst Joachim

doi:10.1139/p01-139

Cited by 31 publications

(34 citation statements)

References 57 publications

(121 reference statements)

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“…This is a classic signal of instability, and corresponds precisely to the vacuum instability of vacuum pair production first noted by Heisenberg and Euler. This imaginary part can also be seen to arise from the poles on the real s axis encountered in the integral representation (1.23), which shows that this integral representation must be defined more carefully, with an approriate iǫ prescription [3,12]. From this integral representation, or from a Borel dispersion relation, it is straightforward to derive the full nonperturbative imaginary part of the Heisenberg-Euler effective Lagrangian to be:…”

Section: Spinor Qed Casementioning

confidence: 99%

“…and a and b are related to the Lorentz invariants a characterizing the background electromagnetic field strength [1]: If G = 0, it is possible to transform to a Lorentz frame in which the electric and magnetic fields are parallel or antiparallel, depending on the sign a There has been a notational reversal [3,8,62] of a ↔ b since the original Heisenberg-Euler paper [1]. I stick here with Heisenberg's original notation since in a frame in which B and E are parallel, we associate b ↔ B and a ↔ E, which seems more natural.…”

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confidence: 99%

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Heisenberg–euler Effective Lagrangians: Basics and Extensions

Dunne

2005

From Fields to Strings: Circumnavigating Theoretical Physics

276

390

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I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum electrodynamics in a constant electromagnetic background field, and then summarizing some of the important applications and generalizations to inhomogeneous background fields, nonabelian backgrounds, and higher loop effective Lagrangians.Dedicated to the memory of Ian Kogan, a great physicist and friend, whose enthusiasm for life and science is sorely missed.

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Section: Spinor Qed Casementioning

confidence: 99%

mentioning

confidence: 99%

Heisenberg–euler Effective Lagrangians: Basics and Extensions

Dunne

2005

From Fields to Strings: Circumnavigating Theoretical Physics

276

390

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“…The n th term in the sum directly relates to the probability for the coherent production of n pairs by the field [17,25]. Usually one derives the formula (1) by a proper treatment of the poles appearing in the standard integral representation of the one-loop Euler-Heisenberg lagrangian (see, e.g., [26,27]). Affleck et al showed in [24] that the same formula can be obtained in the spirit of instanton physics by a stationary phase appromixation of the corresponding worldline path integral.…”

Section: Introductionmentioning

confidence: 99%

Worldline instantons and pair production in inhomogenous fields

Dunne

Schubert²

2005

Phys. Rev. D

307

503

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We show how to do semiclassical nonperturbative computations within the worldline approach to quantum field theory using "worldline instantons". These worldline instantons are classical solutions to the Euclidean worldline loop equations of motion, and are closed spacetime loops parametrized by the proper-time. Specifically, we compute the imaginary part of the one loop effective action in scalar QED using "worldline instantons", for a wide class of inhomogeneous electric field backgrounds. We treat both time dependent and space dependent electric fields, and note that temporal inhomogeneities tend to shrink the instanton loops, while spatial inhomogeneities tend to expand them. This corresponds to temporal inhomogeneities tending to enhance local pair production, with spatial inhomogeneities tending to suppress local pair production. We also show how the worldline instanton technique extends to spinor QED.

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“…Let us also recall that due to an electric-magnetic duality, the Heisenberg-Euler effective Lagrangian and the photon polarization tensor in a purely magnetic and a purely electric field are related and can be translated into each other [26,27]: the magnetic field result is converted into the corresponding electric field result by means of the transformations B ↔ −iE and ↔⊥. Hence, our result (4.20) for Π µν 2-loop (k|B) 1PR can be straightforwardly adapted to a purely electric field, yielding the exact expression for Π µν 2-loop (k|E) 1PR .…”

Section: -Loop Hementioning

confidence: 99%

Tadpole diagrams in constant electromagnetic fields

Karbstein

2017

J. High Energ. Phys.

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Abstract:We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations of the latter class of diagrams with respect to the field strength tensor and contractions with derivatives of the one-particle irreducible part of the Heisenberg-Euler effective Lagrangian in constant fields. Specific examples include the two-loop addendum to the HeisenbergEuler effective action as well as a novel one-loop correction to the charged particle propagator in constant electromagnetic fields discovered recently. As an additional example, the approach devised in the present article is adopted to derive the tadpole contribution to the two-loop photon polarization tensor in constant fields for the first time.

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QED effective action revisited

Cited by 31 publications

References 57 publications

Heisenberg–euler Effective Lagrangians: Basics and Extensions

Heisenberg–euler Effective Lagrangians: Basics and Extensions

Worldline instantons and pair production in inhomogenous fields

Tadpole diagrams in constant electromagnetic fields

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