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Because x = -cos θ is dimensionless, it may be more suitable to call the divergence geometric divergence.
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note
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3(sin Λr - π/2). In Λ → ∞, the fast oscillating piece averages zero and can be dropped.
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34
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note
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That IR divergencies should be canceled in any physical quantities was summarized in quantum chromodynamics (QCD) as two theorems: the Kinoshita-Poggio-Quinn theorem and Kinoshita-Lee-Nauenberg theorem. For nonrelativistic quantum field theories, it was discussed in the context of the FQH effect in Ref. 7 and Ref. 8 and in the context of a superconductor-toinsultaor transition in Ref. 9.
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