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This result has been rederived several times. See ref. 4 and references therein.
In fact this is not a tetrad but an SZ family of null tetrads. See ref. 4 and references therein.
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By fixing a value of ζ we recover the results cited in ref. 15.
To obtain a rigorous limit one should follow the same outlines as in the LSZ formalism, i.e., to average the fields with wave packets.
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Kozameh, C.N. (1986). The holonomy operator in Yang-Mills theory. In: Barut, A.O., Doebner, H.D. (eds) Conformal Groups and Related Symmetries Physical Results and Mathematical Background. Lecture Notes in Physics, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540171630_75
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DOI: https://doi.org/10.1007/3540171630_75
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