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Master formulas for the dressed scalar propagator in a constant field. (English) Zbl 1361.81163
Summary: The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with $$N$$ photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.

##### MSC:
 81V10 Electromagnetic interaction; quantum electrodynamics 81U05 $$2$$-body potential quantum scattering theory 81T18 Feynman diagrams 81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
##### Keywords:
Compton scattering cross section
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##### References:
 [1] Feynman, R. P., Mathematical formulation of the quantum theory of electromagnetic interaction, Phys. Rev., 80, 440, (1950) · Zbl 0040.28002 [2] Strassler, M. J., Field theory without Feynman diagrams: one-loop effective actions, Nucl. Phys. B, 385, 145, (1992) [3] Bern, Z.; Kosower, D. A., Efficient calculation of one loop QCD amplitudes, Phys. Rev. Lett., 66, 1669, (1991) [4] Bern, Z.; Kosower, D. A., The computation of loop amplitudes in gauge theory, Nucl. Phys. B, 379, 451, (1992) [5] Ahmadiniaz, N.; Schubert, C.; Villanueva, V. M., String-inspired representations of photon/gluon amplitudes, J. High Energy Phys., 1301, (2013) [6] Schmidt, M. G.; Schubert, C., Multiloop calculations in the string-inspired formalism: the single spinor-loop in QED, Phys. Rev. D, 53, 2150, (1996) [7] Schubert, C., Perturbative quantum field theory in the string-inspired formalism, Phys. Rep., 355, 73, (2001) · Zbl 0988.81108 [8] Bastianelli, F.; Huet, A.; Schubert, C.; Thakur, R.; Weber, A., Integral representations combining ladders and crossed ladders, J. High Energy Phys., 1407, (2014) [9] Shaisultanov, R. Zh., On the string-inspired approach to QED in external field, Phys. Lett. B, 378, 354, (1996) [10] Reuter, M.; Schmidt, M. G.; Schubert, C., Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals, Ann. Phys. (N.Y.), 259, 313, (1997) · Zbl 0988.81523 [11] Dittrich, W.; Shaisultanov, R., Vacuum polarization in QED with world-line methods, Phys. Rev. D, 62, (2000) [12] Schubert, C., Vacuum polarisation tensors in constant electromagnetic fields: part I, Nucl. Phys. B, 585, 407, (2000) · Zbl 0971.81182 [13] Adler, S. L.; Schubert, C., Photon splitting in a strong magnetic field: recalculation and comparison with previous calculations, Phys. Rev. Lett., 77, 1695, (1996) [14] Fliegner, D.; Reuter, M.; Schmidt, M. G.; Schubert, C., The two-loop Euler-Heisenberg Lagrangian in dimensional renormalization, Teor. Mat. Fiz., Theor. Math. Phys., 113, 1442, (1997) [15] Körs, B.; Schmidt, M. G., The effective two loop Euler-Heisenberg action for scalar and spinor QED in a general constant background field, Eur. Phys. J. C, 6, 175, (1999) [16] Dunne, G. V.; Huet, A.; Rivera, D.; Schubert, C., Closed-form weak-field expansion of two-loop Euler-Heisenberg Lagrangians, J. High Energy Phys., 0611, (2006) [17] Dunne, G. V.; Schubert, C., Two-loop self-dual Euler-Heisenberg Lagrangians. I: real part and helicity amplitudes, J. High Energy Phys., 0208, (2002) · Zbl 1226.81294 [18] Bastianelli, F.; Zirotti, A., Worldline formalism in a gravitational background, Nucl. Phys. B, 642, 372, (2002) · Zbl 0998.81064 [19] Bastianelli, F.; Corradini, O.; Zirotti, A., Dimensional regularization for $$N = 1$$ supersymmetric sigma models and the worldline formalism, Phys. Rev. D, 67, (2003) [20] Bastianelli, F.; Corradini, O.; Zirotti, A., BRST treatment of zero modes for the worldline formalism in curved space, J. High Energy Phys., 0401, (2004) · Zbl 1243.81211 [21] Bastianelli, F.; Schubert, C., One-loop photon-graviton mixing in an electromagnetic field: part 1, J. High Energy Phys., 0502, (2005) [22] Bastianelli, F.; Nucamendi, U.; Schubert, C.; Villanueva, V. M., One-loop photon-graviton mixing in an electromagnetic field: part 2, J. High Energy Phys., 0711, (2007) · Zbl 1140.83345 [23] Bastianelli, F.; Dávila, J. M.; Schubert, C., Gravitational corrections to the Euler-Heisenberg Lagrangian, J. High Energy Phys., 0903, (2009) [24] Bastianelli, F.; Corradini, O.; Dávila, J. M.; Schubert, C., On the low energy limit of one loop photon-graviton amplitudes, Phys. Lett. B, 716, 345, (2012) [25] Daikouji, K.; Shino, M.; Sumino, Y., Bern-kosower rule for scalar QED, Phys. Rev. D, 53, 4598, (1996) [26] Bastianelli, F.; van Nieuwenhuizen, P., Path integrals and anomalies in curved space, (2006), Cambridge University Press · Zbl 1120.81057 [27] Fliegner, D.; Schmidt, M. G.; Schubert, C., The higher derivative expansion of the effective action by the string-inspired method, part I, Z. Phys. C, 64, 111, (1994) [28] Ahmadiniaz, N.; Bashir, A.; Schubert, C., Multiphoton amplitudes and generalized Landau-khalatnikov-Fradkin transformation in scalar QED, Phys. Rev. D, 93, (2016) [29] N. Ahmadiniaz, F. Bastianelli, O. Corradini, J.P. Edwards, C. Schubert, in preparation. [30] Ahmadiniaz, N.; Bastianelli, F.; Corradini, O., Tree-level amplitudes in scalar QCD from the worldline formalism, Phys. Rev. D, 93, (2016) [31] Corradini, O.; Schubert, C., Lectures on the worldline formalism, given at School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and Conformal Geometry, Morelia, Mexico, November 19-23, 2012 [32] Fradkin, E. S.; Gitman, D. M.; Shvartsman, S. M., Quantum electrodynamics with unstable vacuum, (1991), Springer [33] McKeon, D. G.C.; Sherry, T. N., Radiative effects in a constant magnetic field using the quantum mechanical path integral, Mod. Phys. Lett. A, 9, 2167, (1994) [34] Srednicki, M., Quantum field theory, (2007), Cambridge University Press · Zbl 1113.81002 [35] Daugherty, J. K.; Harding, A. K., Compton scattering in strong magnetic fields, Astrophys. J., 309, 362, (1986)
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