Dark Matter and the vacuum energy

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I wonder if there is any correlation between the weak coupling of a quantum field in the path integral and how it adds to or cancels out vacuum energy. If so, then how would weakly interacting dark matter effect the vacuum energy? Thanks.
 
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Why do you suggest that coupling between fields should have anything to do with vacuum energy?
 
And why do you think that dark matter is of special relevance for vacuum enery?
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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