Two-loop Yang–Mills theory in the world-line formalism and an Euler–Heisenberg type action

Sato, Haru–Tada; Schmidt, Michael G.; Zahlten, Claus

doi:10.1016/s0550-3213(00)00220-0

Cited by 26 publications

(24 citation statements)

References 24 publications

(18 reference statements)

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“…the two loop effective Lagrangian for Yang-Mills theory in a constant self-dual quasi-abelian background. The two-loop worldline formulas derived in [29] for the general nonabelian Euler-Heisenberg type Lagrangian should provide a good starting point for its computation.…”

Section: Discussionmentioning

confidence: 99%

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

Dunne¹,

Schubert²

2002

J. High Energy Phys.

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: Discussionmentioning

confidence: 99%

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

Dunne¹,

Schubert²

2002

J. High Energy Phys.

117

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“…non-Abelian generalisation was used in the first calculation of the one-loop five-gluon amplitudes [40], a calculation of the non-Abelian heat-kernel coefficients to fifth order [41], a calculation of the two-loop effective Lagrangian for a constant SU(2) background field [42], and very recently for obtaining gauge-invariant decompositions of the off-shell three-and four-gluon amplitudes [43][44][45][46]. In the non-Abelian case, it may be helpful to generate the particle color factor, and take care of the path ordering, by adding suitable auxiliary fields, in the same way as Grassmann variables take care of the spin factor and path ordering in (1.19) -see, for example, [47][48][49][50].…”

Section: Jhep08(2020)018mentioning

confidence: 99%

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Ahmadiniaz

Guzman

Bastianelli

et al. 2020

J. High Energ. Phys.

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In the first-quantised worldline approach to quantum field theory, a longstanding problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the "N -photon kernel," where offshell this kernel appears also in "subleading" terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

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“…This method [8,9], also related to the infinite tension limit of String theory [10,11], was used heavily for the discussion of various effective actions in one-loop [9,12,13,14] and two-loop [15,16,17,18] order. For example, the high order in the inverse mass calculation of ref.…”

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confidence: 99%

Effective action in a general chiral model: Next to leading order derivative expansion in the worldline method

2008

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Two-loop Yang–Mills theory in the world-line formalism and an Euler–Heisenberg type action

Cited by 26 publications

References 24 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

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Effective action in a general chiral model: Next to leading order derivative expansion in the worldline method

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