# zbMATH — the first resource for mathematics

One-particle reducible contribution to the one-loop spinor propagator in a constant field. (English) Zbl 1373.81401
Summary: Extending work by Gies and Karbstein on the Euler-Heisenberg Lagrangian, it has recently been shown that the one-loop propagator of a charged scalar particle in a constant electromagnetic field has a one-particle reducible contribution in addition to the well-studied irreducible one. Here we further generalize this result to the spinor case, and find the same relation between the reducible term, the tree-level propagator and the one-loop Euler-Heisenberg Lagrangian as in the scalar case. Our demonstration uses a novel worldline path integral representation of the photon-dressed spinor propagator in a constant electromagnetic field background.

##### MSC:
 81V10 Electromagnetic interaction; quantum electrodynamics 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 78A35 Motion of charged particles 81S40 Path integrals in quantum mechanics
Full Text:
##### References:
 [1] Fradkin, E. S.; Gitman, D. M.; Shvartsman, S. M., Quantum electrodynamics with unstable vacuum, (1991), Springer [2] Gies, H.; Karbstein, F., An addendum to the Heisenberg-Euler effective action beyond one loop, J. High Energy Phys., 1703, (2017) · Zbl 1377.83032 [3] Heisenberg, W.; Euler, H., Folgerungen aus der diracschen theorie des positrons, Z. Phys., 98, 714, (1936) · Zbl 0013.18503 [4] Ritus, V. I., Lagrangian of an intense electromagnetic field and quantum electrodynamics at short distances, Zh. Èksp. Teor. Fiz., Sov. Phys. JETP, 42, 774, (1975) [5] Dittrich, W.; Reuter, M., Effective Lagrangians in quantum electrodynamics, (1985), Springer [6] Reuter, M.; Schmidt, M. G.; Schubert, C., Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals, Ann. Phys., 259, 313, (1997) · Zbl 0988.81523 [7] Edwards, J. P.; Schubert, C., One-particle reducible contribution to the one-loop scalar propagator in a constant field, Nucl. Phys. B, 923, 339, (2017) · Zbl 1373.81402 [8] Strassler, M. J., Field theory without Feynman diagrams: one-loop effective actions, Nucl. Phys. B, 385, 145, (1992) [9] Schmidt, M. G.; Schubert, C., On the calculation of effective actions by string methods, Phys. Lett. B, 318, 438, (1993) [10] Schmidt, M. G.; Schubert, C., Multiloop calculations in the string-inspired formalism: the single spinor-loop in QED, Phys. Rev. D, 53, 2150, (1996) [11] Shaisultanov, R. Zh., On the string-inspired approach to QED in external field, Phys. Lett. B, 378, 354, (1996) [12] Adler, S. L.; Schubert, C., Photon splitting in a strong magnetic field: recalculation and comparison with previous calculations, Phys. Rev. Lett., 77, 1695, (1996) [13] Schubert, C., Vacuum polarisation tensors in constant electromagnetic fields: part I, Nucl. Phys. B, 585, 407, (2000) · Zbl 0971.81182 [14] Schubert, C., Perturbative quantum field theory in the string-inspired formalism, Phys. Rep., 355, 73, (2001) · Zbl 0988.81108 [15] Ahmad, A.; Ahmadiniaz, N.; Corradini, O.; Kim, S. P.; Schubert, C., Master formulas for the dressed scalar propagator in a constant field, Nucl. Phys. B, 919, 9, (2017) · Zbl 1361.81163 [16] N. Ahmadiniaz, F. Bastianelli, O. Corradini, J.P. Edwards, C. Schubert, in preparation. [17] Fradkin, E. S.; Gitman, D. M., Path integral representation for the relativistic particle propagators and BFV quantization, Phys. Rev. D, 44, 3230, (1991) [18] Srednicki, M., Quantum field theory, (2007), Cambridge University Press · Zbl 1113.81002 [19] Dittrich, W.; Gies, H., Probing the quantum vacuumperturbative effective action approach in quantum electrodynamics and its application, Springer Tracts Mod. Phys., vol. 166, 1, (2000) [20] Kuznetsov, A.; Mikheev, N., Electroweak processes in external electromagnetic fields, Springer Tracts in Modern Physics, (2004), Springer · Zbl 1058.81734 [21] Ritus, V. I., Method of eigenfunctions and mass operator in quantum electrodynamics of a constant field, Zh. Eksp. Teor. Fiz., J. Exp. Theor. Phys., 48, 788, (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.