Editing World line (section)

==World lines in quantum field theory==
Quantum field theory, the framework in which all of modern particle physics is described, is usually described as a theory of quantized fields. However, although not widely appreciated, it has been known since Feynman<ref>{{cite journal|last = Feynman|first = Richard P.|author-link = Richard Feynman|title = Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction|journal = [[Physical Review]]|year = 1950|volume = 80|issue = 1|pages = 108–128|doi = 10.1103/PhysRev.80.440|url = https://journals.aps.org/pr/abstract/10.1103/PhysRev.80.440}}</ref> that many quantum field theories may equivalently be described in terms of world lines. This preceded much of his work<ref>{{cite journal|last = Feynman|first = Richard P.|author-link = Richard Feynman|title = An operator calculus having applications in quantum electrodynamics|journal = [[Physical Review]]|year = 1951|volume = 84|issue = 3|pages = 440-457|doi = 10.1103/PhysRev.84.108|url = https://authors.library.caltech.edu/3530/1/FEYpr51.pdf|bibcode = 1951PhRv...84..108F}}</ref> on the formulation which later became more standard. The [[Path integral formulation#Quantum field theory|world line formulation of quantum field theory]] has proved particularly fruitful for various calculations in gauge theories<ref>{{cite journal|last1 = Bern|first1 = Zvi|author-link1 = Zvi Bern|first2 = David A.|last2 = Kosower|title = Efficient calculation of one-loop QCD amplitudes|journal = [[Physical Review Letters]]|volume = 66|issue = 13|year = 1991|pages = 1669–1672|pmid = 10043277|doi = 10.1103/PhysRevLett.66.1669|bibcode = 1991PhRvL..66.1669B}}</ref><ref>{{cite journal|last1 = Bern|first1 = Zvi|author-link1 = Zvi Bern|first2 = Lance|last2 = Dixon|author-link2 = Lance J. Dixon|first3 = David A.|last3 = Kosower|title = Progress in one-loop QCD computations|journal = [[Annual Review of Nuclear and Particle Science]]|volume = 46|year = 1996|pages = 109–148|url = http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-7111.pdf|arxiv = hep-ph/9602280|doi = 10.1146/annurev.nucl.46.1.109| doi-access=free|bibcode = 1996ARNPS..46..109B}}</ref><ref>{{cite journal|last = Schubert|first = Christian|title = Perturbative quantum field theory in the string-inspired formalism|journal = [[Physics Reports]]|volume = 355|issue = 2–3|year = 2001|pages = 73–234|doi = 10.1016/S0370-1573(01)00013-8|arxiv = hep-th/0101036|bibcode = 2001PhR...355...73S|s2cid = 118891361}}</ref> and in describing nonlinear effects of electromagnetic fields.<ref>{{cite journal|last1 = Affleck|first1 = Ian K.|author-link1 = Ian Affleck|first2 = Orlando|last2 = Alvarez|first3 = Nicholas S.|last3 = Manton|author-link3 = Nicholas S. Manton|title = Pair production at strong coupling in weak external fields|journal = [[Nuclear Physics B]]|volume = 197|issue = 3|year = 1982|pages = 509–519|doi = 10.1016/0550-3213(82)90455-2|bibcode = 1982NuPhB.197..509A}}</ref><ref>{{cite journal|last1 = Dunne|first1 = Gerald V.|first2 = Christian|last2 = Schubert|title = Worldline instantons and pair production in inhomogenous fields|journal = [[Physical Review D]]|volume = 72|issue = 10|year = 2005|page = 105004|doi = 10.1103/PhysRevD.72.105004|arxiv = hep-th/0507174|url = https://cds.cern.ch/record/855960/files/0507174.pdf?version=1|bibcode = 2005PhRvD..72j5004D|s2cid = 119357180}}</ref>