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Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculationin the unitary gauge for the $H \to \gamma \gamma$ process via one W loop isrepeated, but without the specific choice of the independent loop momentum forthe Feynman diagrams. This is based on the original 'Dyson scheme' provided inDyson's classical paper. I.e., the original integrations on all propagatormomenta are kept, not expressed by the specified independent loop momentum.Correspondingly, the 4-dimension $\delta$ function at each vertex in which the4-momentum conservation is embedded, is retained. Together with the Wardidentity of the W-W-photon vertex, the 4-momentum conservation of each vertexguarantee the cancellation of all divergent integrals worse than logarithmicwithout any uncertainty or ambiguity, with any shift of integrated momentumeschewed. The calculation is in 4-dimension Minkowski phase space and withoutany help of regularization. The resulting integrals are to the mostlogarithmically divergent, hence is invariant for various setting of theindependent loop momentum and any of its shift. At last the logarithmicallydivergent symmetric (tensor) integration is determined by the boundarycondition at infinity in momentum space inherent of the free Feynmanpropagator, and the gauge (both $SU(2)\times U_Y(1)$ and $U_{em}(1)$) invariantfinite result can be obtained without the introduction of the 'Dysonsubtraction'. The physical boundary conditions at infinity of phase space canmake sense in many problems.

Unambiguous cancellation of divergences of $H \to \gamma \gamma$ process  via one W loop in unitary gauge: Gauge invariance in Dyson scheme and  physical boundary condition