Editing Quantum field theory (section)

=== Source theory ===
Schwinger, however, took a different route. For more than a decade he and his students had been nearly the only exponents of field theory,<ref name=MiltonMehra/>{{rp|p=454}} but in 1951<ref>{{Cite journal |last=Schwinger |first=Julian |date=July 1951 |title=On the Green's functions of quantized fields. I |journal=Proceedings of the National Academy of Sciences |language=en |volume=37 |issue=7 |pages=452–455 |doi=10.1073/pnas.37.7.452 |issn=0027-8424 |pmc=1063400 |pmid=16578383 |doi-access=free |bibcode=1951PNAS...37..452S }}</ref><ref>{{Cite journal |last=Schwinger |first=Julian |date=July 1951 |title=On the Green's functions of quantized fields. II |journal=Proceedings of the National Academy of Sciences |language=en |volume=37 |issue=7 |pages=455–459 |doi=10.1073/pnas.37.7.455 |issn=0027-8424 |pmc=1063401 |pmid=16578384 |doi-access=free |bibcode=1951PNAS...37..455S }}</ref> he found a way around the problem of the infinities with a new method using ''external sources'' as currents coupled to gauge fields.<ref>{{Cite journal |last=Schweber |first=Silvan S. |date=2005-05-31 |title=The sources of Schwinger's Green's functions |journal=Proceedings of the National Academy of Sciences |language=en |volume=102 |issue=22 |pages=7783–7788 |doi=10.1073/pnas.0405167101 |issn=0027-8424 |pmc=1142349 |pmid=15930139 |doi-access=free }}</ref> Motivated by the former findings, Schwinger kept pursuing this approach in order to "quantumly" generalize the [[Lagrangian mechanics#Lagrange multipliers and constraints|classical process]] of coupling external forces to the configuration space parameters known as Lagrange multipliers. He summarized his [[Source field|source theory]] in 1966<ref>{{cite journal |last1=Schwinger |first1=Julian |title=Particles and Sources |journal=Phys Rev |date=1966 |volume=152 |issue=4 |page=1219|doi=10.1103/PhysRev.152.1219 |bibcode=1966PhRv..152.1219S }}</ref> then expanded the theory's applications to quantum electrodynamics in his three volume-set titled: ''Particles, Sources, and Fields.''<ref name="Perseus Books" /><ref>{{Cite book |last=Schwinger |first=Julian |title=Particles, sources, and fields. 2 |date=1998 |publisher=Advanced Book Program, Perseus Books |isbn=978-0-7382-0054-5 |edition=1. print |location=Reading, Mass}}</ref><ref>{{Cite book |last=Schwinger |first=Julian |title=Particles, sources, and fields. 3 |date=1998 |publisher=Advanced Book Program, Perseus Books |isbn=978-0-7382-0055-2 |edition=1. print |location=Reading, Mass}}</ref> Developments in pion physics, in which the new viewpoint was most successfully applied, convinced him of the great advantages of mathematical simplicity and conceptual clarity that its use bestowed.<ref name="Perseus Books">{{cite book |last1=Schwinger |first1=Julian |title=Particles, Sources and Fields vol. 1 |date=1998 |publisher=Perseus Books |location=Reading, MA |isbn=0-7382-0053-0 |page=xi}}</ref>

In source theory there are no divergences, and no renormalization. It may be regarded as the calculational tool of field theory, but it is more general.<ref>{{cite book |editor=C.R. Hagen |display-editors=etal |title=Proc of the 1967 Int. Conference on Particles and Fields |date=1967 |publisher=Interscience |location=NY |page=128}}</ref>  Using source theory, Schwinger was able to calculate the anomalous magnetic moment of the electron, which he had done in 1947, but this time with no ‘distracting remarks’ about infinite quantities.<ref name=MiltonMehra/>{{rp|p=467}}

Schwinger also applied source theory to his QFT theory of gravity, and was able to reproduce all four of Einstein's classic results: gravitational red shift, deflection and slowing of light by gravity, and the perihelion precession of Mercury.<ref>{{cite book |last1=Schwinger |first1=Julian |title=Particles, Sources and Fields vol. 1 |date=1998 |publisher=Perseus Bookks |location=Reading, MA |pages=82–85}}</ref>  The neglect of source theory by the physics community was a major disappointment for Schwinger:<blockquote>The lack of appreciation of these facts by others was depressing, but understandable.  -J. Schwinger<ref name="Perseus Books"/></blockquote>See "[[Julian Schwinger#Career|the shoes incident]]" between J. Schwinger and [[Steven Weinberg|S. Weinberg]].<ref name=MiltonMehra>{{Cite book |last1=Milton |first1=K. A. |url=https://books.google.com/books?id=9SmZSN8F164C |title=Climbing the Mountain: The Scientific Biography of Julian Schwinger |last2=Mehra |first2=Jagdish |date=2000 |publisher=Oxford University Press |isbn=978-0-19-850658-4 |edition=Repr |location=Oxford |language=en}}</ref>