Abstract: The main results the thesis are mainly based on my recent article ”Hilbert space inner products for PT-symmetric
Su-Schrieffer-Heeger models” in Int. J. Phys. A correspondence is established between a discretized Laplacian with
imaginary Robin boundary conditions, and the PT-symmetric Su-Schrieffer-Heeger model used in solid state physics.
The latter multi-parametric model is explored in depth, and for a number of special cases, a complete family of
pseudometrics is constructed in a closed form extrapolating to any dimension n of the (finite-dimensional) model.
When complemented with a condition of positivity, the pseudometrics determine all the physical inner products of
the considered model.
