Abstract
The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.
Highlights
In 1948 Casimir and Polder published a long, technically complex paper about the influence of retardation on the van der Waals force [1]
We review our generalisation of the boundary conditions (BCs) employed in the calculation of the Casimir effect associated with the spin-1/2 and spin-1 fields
We have shown that the generalised BCs imply that the allowed values of energy–momentum between two perfectly reflecting parallel plates are the same for all fermionic fields and the same for all bosonic fields
Summary
In 1948 Casimir and Polder published a long, technically complex paper about the influence of retardation on the van der Waals force [1]. Just as in the electromagnetic case, the bag boundary condition modifies the vacuum fluctuations of the field, which results in the appearance of a Casimir force [14,15,16,17,18]. This force, very weak at a macroscopic scale, can be significant on the small length scales encountered in nuclear physics.
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