Quantum vacuum interaction between two sine-Gordon kinks

We calculate the quantum vacuum interaction energy between two kinks of the sine-Gordon equation. Using the TGTG formula, the problem is reduced to the known formulas for quantum fluctuations in the background of a single kink. This interaction induces an attractive force between the kinks in parallel to the Casimir force between conducting mirrors. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to 'Applications of zeta functions and other spectral functions in mathematics and physics'.