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These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and Conformal Geometry, held at Morelia, Mexico, from November 19 through November 23, 2012.
N. Ahmadiniaz, J. P. Edwards and A. Ilderton, “Reducible contributions to quantum electrodynamics in external fields”, JHEP 05
1901
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N. Ahmadiniaz, F. M. Balli, O. Corradini, J. M. Dávila and C. Schubert, “Compton-like scattering of a scalar particle with N N photons and one graviton”, Nucl. Phys. B 950
1908
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J. P. Edwards and C. Schubert, “Quantum mechanical path integrals in the first quantised approach to quantum field theory”, arXiv: 1912.10004 [hep-th]
1912
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R. P. Feynman, “Mathematical formulation of the quantum theory of electromagnetic interaction”, Phys. Rev. 80
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R. P. Feynman, “An Operator calculus having applications in quantum electrodynamics”, Phys. Rev. 84
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R. P. Feynman and A. R. Hibbs, “Quantum Mechanics and Path Integrals”, New York: McGraw-Hill (1965)
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E. S. Fradkin, “Application of functional methods in quantum field theory and quantum statistics (II)”, Nucl. Phys. 76
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L. Brink, S. Deser, B. Zumino, P. Di Vecchia, P. Howe, “Local Supersymmetry for Spinning Particles”, Phys. Lett. B 64
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F. A. Berezin, M. S. Marinov, “Particle spin dynamics as the Grassmann variant of classical mechanics”, Ann. Phys. (N.Y.) 104
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L. Brink, P. Di Vecchia and P. Howe, “A Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles”, Nucl. Phys. B 118
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S. W. Hawking, “Zeta Function Regularization of Path Integrals in Curved Space-Time”, Commun. Math. Phys. 55
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C. Itzykson and J. B. Zuber, “Quantum Field Theory”, McGraw-Hill (1980)
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L. S. Schulman, “Techniques And Applications Of Path Integration”, Wiley (1981)
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I. K. Affleck, O. Alvarez and N. S. Manton, “Pair Production At Strong Coupling In Weak External Fields”, Nucl. Phys. B 197
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C. Itzykson, J. Zuber, “Quantum Field Theory”, McGraw-Hill (1985)
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J. Polchinski, “Evaluation of the One Loop String Path Integral”, Commun. Math. Phys. 104
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J. W. Negele and H. Orland, “Quantum Many Particle Systems”, Frontiers in Physics, 68, Addison-Wesley (1988)
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E. S. Fradkin and D. M. Gitman, “Path integral representation for the relativistic particle propagators and BFV quantization”, Phys. Rev. D 44
1991
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Z. Bern and D. A. Kosower, “Efficient calculation of one loop QCD amplitudes”, Phys. Rev. Lett. 66
1992
Earlier work this paper cites.
M. J. Strassler, “Field theory without Feynman diagrams: One-loop effective actions”, Nucl. Phys. B 385
1992
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F. Bastianelli, “The Path integral for a particle in curved spaces and Weyl anomalies”, Nucl. Phys. B 376
1992
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F. Bastianelli and P. van Nieuwenhuizen, “Trace anomalies from quantum mechanics”, Nucl. Phys. B 389
1993
Earlier work this paper cites.
A. G. Morgan, “Second order fermions in gauge theories,” Phys. Lett. B 351
1995
Cited alongside, same era.
M. G. Schmidt and C. Schubert, “Multiloop calculations in the string inspired formalism: The single spinor loop in QED”, Phys. Rev. D 53
1996
Cited alongside, same era.
S.L. Adler and C. Schubert, “Photon splitting in a strong magnetic field: Recalculation and comparison with previous calculations”, Phys. Rev. Lett. 77
1996
Cited alongside, same era.
K. Daikouji, M. Shino, and Y. Sumino, “Bern-Kosower rule for scalar QED,” Phys. Rev. D 53
1996
Cited alongside, same era.
M. Reuter, M. G. Schmidt and C. Schubert, “Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals”, Annals Phys. 259
1997
Cited alongside, same era.
T. J. Hollowood and G. M. Shore, “Causality and Micro-Causality in Curved Spacetime”, Phys. Lett. B 655
2007
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P. Dai, Y. -t. Huang and W. Siegel, “Worldgraph Approach to Yang-Mills Amplitudes from N=2 Spinning Particle”, JHEP 0810
2008
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F. Bastianelli, O. Corradini, P. A. G. Pisani and C. Schubert, “Scalar heat kernel with boundary in the worldline formalism”, JHEP 0810
2008
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O. Corradini and G. D. Esposti, “Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle”, Nucl. Phys. B 970
2008
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F. Bastianelli, J. M. Dávila and C. Schubert, “Gravitational corrections to the Euler-Heisenberg Lagrangian”, JHEP 0903
2009
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C. Schubert, “Vacuum polarisation tensors in constant electromagnetic fields: Part I”, Nucl. Phys. B 585
2000
Cited alongside, same era.
W. Dittrich and H. Gies, “Probing the Quantum Vacuum. Perturbative Effective Action Approach in Quantum Electrodynamics and its Application”, Springer Tracts Mod. Phys. 166
2000
Cited alongside, same era.
M. Chaichian and A. Demichev, “Path integrals in physics. Vol. 1: Stochastic processes and quantum mechanics”, Bristol, UK: IOP (2001)
2001
Cited alongside, same era.
C. Schubert, “Perturbative quantum field theory in the string inspired formalism”, Phys. Rept. 355
2001
Cited alongside, same era.
A. I. Davydychev, P. Osland, and L. Saks, “Quark gluon vertex in arbitrary gauge and dimension”, Phys. Rev. D 63
2001
Cited alongside, same era.
G. V. Dunne and C. Schubert, “Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background”, Phys. Lett. B 526
2002
Cited alongside, same era.
H. Gies, K. Langfeld and L. Moyaerts, “Casimir effect on the worldline”, JHEP 0306
2003
Cited alongside, same era.
F. Bastianelli, O. Corradini and E. Latini, “Spinning particles and higher spin fields on (A)dS backgrounds”, JHEP 0811
2010
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J. Nicasio, J. P. Edwards, C. Schubert and N. Ahmadiniaz, “Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics”, arXiv: 2010.04160 [hep-th]
2010
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F. Bastianelli, R. Bonezzi, O. Corradini and E. Latini, “Effective action for higher spin fields on (A)dS backgrounds”, JHEP 1212
2012
Later among the works it cites.
N. Ahmadiniaz, J. P. Edwards, J. Nicasio and C. Schubert, “Generalized Landau-Khalatnikov-Fradkin transformations for arbitrary N-point fermion correlators”, Phys. Rev. D 104
2012
Later among the works it cites.
N. Ahmadiniaz, C. Schubert and V.M. Villanueva, “String-inspired representations of photon/gluon amplitudes”, JHEP 1301
2013
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N. Ahmadiniaz and C. Schubert, “Covariant representation of the Ball-Chiu vertex”, Nucl. Phys. B 869
2013
Later among the works it cites.
F. Bastianelli, A. Huet, C. Schubert, R. Thakur, and A. Weber, “Integral representations combining ladders and crossed-ladders”, JHEP 07
2014
Later among the works it cites.
R. Bonezzi, O. Corradini, S. A. Franchino Vinas and P. A. G. Pisani, “Worldline approach to noncommutative field theory”, J. Phys. A 45
2015
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J. P. Edwards and P. Mansfield, “Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory,” JHEP 01
2015
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N. Ahmadiniaz and C. Schubert, “QCD gluon vertices from the string-inspired formalism”, International Journal of Modern Physics E. 25
2016
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N. Ahmadiniaz, A. Bashir, and C. Schubert, “Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED,” Phys. Rev. D 93
2016
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N. Ahmadiniaz, F. Bastianelli, and O. Corradini, “Dressed scalar propagator in a non-Abelian background from the worldline formalism”, Phys. Rev. D 93
2016
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A. Ahmad, N. Ahmadiniaz, O. Corradini, S. P. Kim, and C. Schubert, “Master formulas for the dressed scalar propagator in a constant field”, Nucl. Phys. B 919
2017
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J. P. Edwards and C. Schubert, “One-particle reducible contribution to the one-loop scalar propagator in a constant field”, Nucl. Phys. B 923
2017
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N. Ahmadiniaz, F. Bastianelli, O. Corradini, J. P. Edwards and C. Schubert, “One-particle reducible contribution to the one-loop spinor propagator in a constant field”, Nucl. Phys. B 924
2017
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H. Gies and F. Karbstein, “An Addendum to the Heisenberg-Euler effective action beyond one loop”, JHEP 03
2017
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F. Karbstein, “Tadpole diagrams in constant electromagnetic fields,” JHEP 10
2017
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J. P. Edwards, A. Huet and C. Schubert, “On the low-energy limit of the QED N-photon amplitudes: part 2”, Nucl. Phys. B 935
2018
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J. P. Edwards and C. Schubert, “N-photon amplitudes in a plane-wave background”, Phys. Lett. B 822
2021
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