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If memory serves me right, some years ago I heard rumors about developing methods of computing the Casimir force which are rigorous (by the standards of constructive quantum field theory). I become interested in this subject more recently, but it seems there is no way to find it in the flood created by physicists. (I really did not find a single paper.) Does anyone know relevant references?

[EDIT] Now that I think about it, this question may be misunderstood. What I mean are, of course, methods of calculating the Casimir force in nontrivial cases. (Such as complex geometry or two parallel but inhomogeneous plates.) There is a vast physical literature about this.

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Casimir Energy of a Ball and Cylinder in the Zeta Function Technique, 1998.

With this technique one succeeds, specifically, in justifying, in mathematically rigorous way, the appearance of the contribution to the Casimir energy for perfectly conducting spherical and cylindrical shells.

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    $\begingroup$ Thank you. This is an interesting work I did not know about. However, it may be not what I meant. While published in Journal of Mathematical Physics, this seems to me a work on the physical level of rigor. There seems to be no proof, in the paper or in references, that the method they use produces a correct result. (Even if there is little doubt that it does.) $\endgroup$
    – Alex Gavrilov
    Commented Apr 7, 2018 at 16:43

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