  In this work, we consider the Casimir effect due to massless fermionic fields
in the presence of long cylinders. More precisely, we consider the interaction
between a cylinder parallel to a plate, between two parallel cylinders outside
each other, and between a cylinder lying parallelly inside another cylinder. We
derive the explicit formulas for the Casimir interaction energies and compute
the leading and the next-to-leading order terms of the small separation
asymptotic expansions. As expected, the leading order terms coincide with the
proximity force approximations. We compare the results of the next-to-leading
order terms of different quantum fields, and show that our results support the
ansatz of derivative expansions.
