Constant External Fields in Gauge Theory and the Spin 0, 12, 1 Path Integrals

Reuter, Martin; Schmidt, Michael G.; Schubert, Christian

doi:10.1006/aphy.1997.5716

Cited by 209 publications

(327 citation statements)

References 90 publications

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“…Using the exact propagators in a constant field found by Fock [13] and Schwinger [9], and a proper-time cutoff as the UV regulator, Ritus obtained the corresponding two-loop effective Lagrangians L (2) scal,spin in terms of certain two-parameter integrals. Similar two-parameter integral representations for L (2) scal,spin where obtained later by other authors, using either proper-time [14,15] or dimensional regularisation [16,17]. Unfortunately, all of these double parameter integral representations are quite complicated, so that it is much more difficult to study the weak-and strong-field expansions at two-loops than at one-loop.…”

Section: Introduction: Qed and Qcd In Constant Fieldsmentioning

confidence: 52%

“…In [15,16] the two-loop Euler-Heisenberg Lagrangian in (Euclidean) Scalar QED was obtained in terms of the following fourfold parameter integral,…”

Section: Scalar Qedmentioning

confidence: 99%

“…They are expressed in terms of the worldline Green's function G B and its first and second derivatives [15]:…”

Section: Scalar Qedmentioning

confidence: 99%

“…For the two-loop Euler-Heisenberg Lagrangian in Euclidean spinor QED, the worldline formalism leads to the following parameter integral, which is completely analogous to (3.4) [15,16]:…”

Section: Spinor Qedmentioning

confidence: 99%

“…The calculation, together with the charge and mass renormalization, proceed in a manner analogous to the two-loop scalar QED calculation in the previous section (for details of the mass renormalization, see [15]). After similar manipulations we find that the on-shell renormalized effective Lagrangian can be written as the following proper-time integral:…”

Section: Spinor Qedmentioning

confidence: 99%

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Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

Dunne¹,

Schubert²

2002

J. High Energy Phys.

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117

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We show that, for both scalar and spinor QED, the two-loop Euler-Heisenberg effective Lagrangian for a constant Euclidean self-dual background has an extremely simple closed-form expression in terms of the digamma function. Moreover, the scalar and spinor QED effective Lagrangians are very similar to one another. These results are dramatic simplifications compared to the results for other backgrounds. We apply them to a calculation of the low energy limits of the two-loop massive N-photon 'all +' helicity amplitudes. The simplicity of our results can be related to the connection between self-duality, helicity and supersymmetry.

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Section: Introduction: Qed and Qcd In Constant Fieldsmentioning

confidence: 52%

“…In [15,16] the two-loop Euler-Heisenberg Lagrangian in (Euclidean) Scalar QED was obtained in terms of the following fourfold parameter integral,…”

Section: Scalar Qedmentioning

confidence: 99%

“…They are expressed in terms of the worldline Green's function G B and its first and second derivatives [15]:…”

Section: Scalar Qedmentioning

confidence: 99%

“…For the two-loop Euler-Heisenberg Lagrangian in Euclidean spinor QED, the worldline formalism leads to the following parameter integral, which is completely analogous to (3.4) [15,16]:…”

Section: Spinor Qedmentioning

confidence: 99%

Section: Spinor Qedmentioning

confidence: 99%

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Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

Dunne¹,

Schubert²

2002

J. High Energy Phys.

Self Cite

117

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The Feynman–Schwinger Representation in QCD

Simonov

Tjon

2002

Annals of Physics

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The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative background and valence gluon part. For nonperturbative contributions the background perturbation theory is used systematically, yielding two types of expansions, illustrated by direct physical applications. As an application, we discuss the collinear singularities in the FeynmanSchwinger representation formalism. Moreover, the generalization to nonzero temperature is made and expressions for partition functions in perturbation theory and nonperturbative background are explicitly written down. C 2002 Elsevier Science (USA)

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String-inspired representations of photon/gluon amplitudes

Ahmadiniaz

Schubert

Villanueva

2013

J. High Energ. Phys.

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The string-based Bern-Kosower rules provide an efficient way for obtaining parameter integral representations of the one-loop N - photon/gluon amplitudes involving a scalar, spinor or gluon loop, starting from a master formula and using a certain integration-by-parts (`IBP') procedure. Strassler observed that this algorithm also relates to gauge invariance, since it leads to the absorption of polarization vectors into field strength tensors. Here we present a systematic IBP algorithm that works for arbitrary N and leads to an integrand that is not only suitable for the application of the Bern-Kosower rules but also optimized with respect to gauge invariance. In the photon case this means manifest transversality at the integrand level, in the gluon case that a form factor decomposition of the amplitude into transversal and longitudinal parts is generated naturally by the IBP, without the necessity to consider the nonabelian Ward identities. Our algorithm is valid off-shell, and provides an extremely efficient way of calculating the one-loop one-particle-irreducible off-shell Green's functions (`vertices') in QCD. It can also be applied essentially unchanged to the one-loop gauge boson amplitudes in open string theory. In the abelian case, we study the systematics of the IBP also for the practically important case of the one-loop N - photon amplitudes in a constant field.Comment: 27 pages, no figures, v2 corrects typos in eqs. (3.7) and (4.11

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Constant External Fields in Gauge Theory and the Spin 0, 12, 1 Path Integrals

Cited by 209 publications

References 90 publications

Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

The Feynman–Schwinger Representation in QCD

String-inspired representations of photon/gluon amplitudes

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