# Furry's theorem

Furry's theorem A triangle diagram, if all photons are real, this diagram is forbidden by Furry's theorem.

In quantum electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines connected to an odd number of vertices, its contribution vanishes. As a corollary, no single photon can arise or be destroyed from the vacuum state.[1] The theorem was first derived by Wendell H. Furry in 1937,[2] as a direct consequence of the conservation of energy and charge invariance (C-symmetry).

Furry's theorem is based on the invariance of the vacuum under charge conjugation and the symmetry of the photon-fermion vertex under such. It is therefore not valid for non-Abelian gauge theories in which C-odd contributions also occur. For example, a scattering of three real gluons is not forbidden in quantum chromodynamics, but is instead proportional to the structure constant of the associated Lie algebra.[3] See also Ward–Takahashi identity Wick's theorem References ^ Peskin, Michael E. (2018-05-04). An Introduction To Quantum Field Theory. CRC Press. ISBN 978-0-429-97210-2. ^ Furry, W. H. (1937-01-15). "A Symmetry Theorem in the Positron Theory". Physical Review. 51 (2): 125–129. doi:10.1103/PhysRev.51.125. ISSN 0031-899X. ^ Smolyakov, N. V. (1982). "Furry theorem for non-abelian gauge Lagrangians". Theoretical and Mathematical Physics. 50 (3): 225–228. doi:10.1007/BF01016449. ISSN 0040-5779. S2CID 119765674. hide vte Quantum electrodynamics Formalism Euler–Heisenberg LagrangianFeynman diagramGupta–Bleuler formalismPath integral formulation Particles Dual photonElectronPhotonPositronPositroniumVirtual particles Concepts Anomalous magnetic dipole momentFurry's theoremKlein–Nishina formulaLandau poleQED vacuumSchwinger limitUehling potentialVacuum polarizationVertex functionWard–Takahashi identity Processes Bhabha scatteringBreit–Wheeler processBremsstrahlungCompton scatteringDelbrück scatteringLamb shiftMøller scatteringSchwinger effectPhoton-photon scattering See also: Template:Quantum mechanics topics This electromagnetism-related article is a stub. You can help Wikipedia by expanding it.

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