  Following the seminal works of Asorey-Ibort-Marmo and
Mu\~{n}oz-Casta\~{n}eda-Asorey about selfadjoint extensions and quantum fields
in bounded domains, we compute all the heat kernel coefficients for any
strongly consistent selfadjoint extension of the Laplace operator over the
finite line $[0,L]$. The derivative of the corresponding spectral zeta function
at $s=0$ (partition function of the corresponding quantum field theory) is
obtained. In order to compute the correct expression for the $a_{1/2}$ heat
kernel coefficient, it is necessary to know in detail which non-negative
selfadjoint extensions have zero modes and how many of them they have. The
answer to this question leads us to analyse zeta function properties for the
Von Neumann-Krein extension, the only extension with two zero modes.
