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Reports on Mathematical Physics 69, 331-351 (2012)


General formula for symmetry factors of Feynman Diagrams

L.T. Hue, H.T. Hung and H.N. Long

General formula for symmetry factors (S-factor) of Feynman diagrams containing fields with high spins is derived. We prove that symmetry factors of Feynman diagrams of wellknown theories do not depend on spins of fields. In contributions to S-factors, slf-conjugate fields and non-self-conjugate fields play the same roles as real scalar fields and complex scalar fields, respectively. Thus, the formula of S-factors for scalar theories—theories include only real and complex scalar fields—works on all well-known theories of fields with high spins. Two interesting consequences deduced from our result are: (i) S-factors of all external connected diagrams consisting of only vertices with three different fields, e.g. spinor QED, are equal to unity; (ii) some diagrams with different topologies can contribute the same factor, leading to the result that the inverse S-factor for the total contribution is the sum of inverse S-factors, i.e.