worldline formalism

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The worldline formalism refers to a first-quantized approach to quantum field theory that traces back to work by Fock [1][1], by Feynman on scalar[2] spinor and QED[3], and Schwinger[4]. It is sometimes referred to as "string inspired".

Contents

Scalar fields

Spinor fields

[5] [6] [7]

Vector fields

[8] [9] [10] [11] [12]

A good treatment including gauge bosons is given in [13]. [14]

Bern-Kosower formalism

[15] [16]

See also

References

Reviews: [14] [17]

[1] [18] [2] [3] [4] [19] [20]

[21] [22] [23] [24] [25]

  1. ↑ 1.0 1.1 1.2 V.A. Fock (1937). "{{{title}}}". Izvestiya Akad. Nauk USSR, OMEN: 557. 
  2. ↑ 2.0 2.1 R.P. Feynman (1950). "Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction". Phys. Rev. 80: 440. DOI:10.1103/PhysRev.80.440. 
  3. ↑ 3.0 3.1 R.P. Feynman (1951). "An Operator Calculus Having Applications in Quantum Electrodynamics". Phys. Rev. 84: 108. DOI:10.1103/PhysRev.84.108. 
  4. ↑ 4.0 4.1 Julian Schwinger (1951). "On Gauge Invariance and Vacuum Polarization". Phys. Rev.: 664-679. 
  5. ↑ L. Brink, P. Di Vecchia and P. Howe (1977). "Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles". Nucl. Phys. B 118: 76. DOI:10.1016/0550-3213(77)90364-9. 
  6. ↑ F. A. Berezin and M. S. Marinov (1975). "Classical spin and Grassmann algebra". JETP Lett. 21: 320. 
  7. ↑ R. Casalbuoni (1976). "The classical mechanics for Bose-Fermi systems". Nuovo Cimento A 33: 389. DOI:10.1007/BF02729860. 
  8. ↑ F. Bastianelli (2005). "Worldline approach to vector and antisymmetric tensor fields". JHEP 0504. arXiv:hep-th/0503155. DOI:10.1088/1126-6708/2005/04/010. 
  9. ↑ F. Bastianelli (2005). "Worldline approach to vector and antisymmetric tensor fields. II.". JHEP 0510. arXiv:hep-th/0510010. DOI:10.1088/1126-6708/2005/10/114. 
  10. ↑ Ryusuke Endo. "Gauge Dependence of the Grabvitational Conformal Anomaly for the Electromagnetic Field". Prog.Theor.Phys. 71: 1366-1984. DOI:10.1143/PTP.71.1366. 
  11. ↑ Kim Milton (ed.), Giuseppe Bimonte, Enrico Calloni, Luciano Di Fiore, Giampiero Esposito, Leopoldo Milano, Luigi Rosa (2004). "Photon Green Functions in Curved Space-Time", Published in Quantum Field Theory Under the Influence of External Conditions: Proceedings. Rinton Press, 358-363. ISBN ISBN 1-58949-033-9. 
  12. ↑ V O Rivelles, L Sandoval Jr (1991). "BRST quantization of relativistic spinning particles with a Chern-Simons term". Class. Quantum Grav. 8: 1605-1612. DOI:10.1088/0264-9381/8/8/022. 
  13. ↑ M. Reuter, M. G. Schmidt, C. Schubert (1997). "Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals". Annals Phys 259: 313-365. arXiv:hep-th/9610191. DOI:10.1006/aphy.1997.5716. 
  14. ↑ 14.0 14.1 M. Strassler (1992). "Field theory without Feynman diagrams: One loop effective actions". Nucl.Phys.B 385: 145-184. arXiv:hep-ph/9205205. DOI:10.1016/0550-3213(92)90098-V. 
  15. ↑ Z. Bern and D.A. Kosower (1991). "Efficient calculation of one-loop QCD amplitudes". Phys. Rev. Lett. 66: 1669. DOI:10.1103/PhysRevLett.66.1669. 
  16. ↑ Z. Bern and D.A. Kosower (1992). "The computation of loop amplitudes in gauge theories". Nucl. Phys. B 379: 451. DOI:10.1016/0550-3213(92)90134-W. 
  17. ↑ C. Schubert (2001). "Perturbative Quantum Field Theory in the String-Inspired Formalism". Phys.Rept. 355: 73-234. arXiv:hep-th/0101036. DOI:10.1016/S0370-1573(01)00013-8. 
  18. ↑ V. A. Fock (1937). "Die Eigenzeit in der klassischen und in der Quantenmechanik". Phyz. Z. Sow. 12: 404–425. 
  19. ↑ Christian Schubert (2001). "Perturbative Quantum Field Theory in the String-Inspired Formalism". Phys.Rept. 355: 73-234. arXiv:hep-th/0101036v2. 
  20. ↑ Christian Schubert. "QED in the worldline representation". arXiv:hep-th/0703186v2. 
  21. ↑ Z. Bern, D.A. Kosower (1991). "Color decomposition of one-loop amplitudes in gauge theories". Nucl. Phys. B 362: 389. 
  22. ↑ Z. Bern, D.A. Kosower (1992). "The computation of loop amplitudes in gauge theories". Nucl. Phys. B 379: 451. 
  23. ↑ M.J. Strassler (1992). "Field theory without Feynman diagrams: One-loop effective actions". Nucl. Phys. B 385: 145. arXiv:hep-ph/9205205. 
  24. ↑ M.B. Halpern, W. Siegel (1977). "The Particle Limit of Field Theory: A New Strong Coupling Expansion". Phys.Rev.D 16: 2486. DOI:10.1103/PhysRevD.16.2486. 
  25. ↑ Michael G. Schmidt, Christian Schubert (1994). "The Worldline path integral approach to Feynman graphs". arXiv:hep-ph/9412358. 
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