Unified boundary conditions and Casimir forces for fields with arbitrary spin

The electromagnetic Casimir effect is well-known and has been extensively studied for the last half-century. This attractive force between parallel plates arises from the imposition of boundary conditions upon the fluctuating spin-1 photon field, so a natural further question is wether fields of different spin can cause similar forces when confined in the same way. However, so far it has not been clear what the appropriate boundary conditions for physically-confined spinor fields may be. Here we present work that generalises the physically well-motivated electromagnetic boundary conditions to fields of arbitrary spin, thus arriving at physically reasonable boundary conditions\footnote{A. Stokes and R. Bennett, New J. Phys. 17 073012 (2015)} and Casimir forces\footnote{A. Stokes and R. Bennett, Ann. Phys NY 360 246 (2015)} for a selection of interesting fields. For example, the so-called `bag model' boundary conditions from nuclear physics emerge from our generalised boundary condition as a special case, as do the linearised gravity boundary conditions suggested in a remarkable recent proposal\footnote{James Q. Quach, Phys. Rev. Lett. 114 081104 (2015)} concerning possible measurement of gravitonic Casimir forces.