The Casimir effect for fields with arbitrary spin

Abstract

The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are applicable to a field possessing any spin, and include the well-known spin-1/2 and spin-1 boundary conditions as special cases. Here we use these general boundary conditions to show that the allowed values of energy-momentum turn out to be the same for any massless fermionic field and the same for any massless bosonic field. As a result one expects to obtain only two possible Casimir forces, one associated with fermions and the other with bosons. We explicitly verify that this is the case for the fields up to spin-2. A significant implication of our work is that periodic boundary conditions cannot be applied to a fermionic field confined between two parallel plates

The case for a Casimir cosmology

“…The calculation [57] was done for electromagnetic fields. Assuming the same principal behaviour for the other bosonic fields of the Standard Model would amount to multiplying equation (4.3) with the number of the independent field components divided by two (the polarizations of the electromagnetic field) [43] ([61] and references therein). As the precise cut-off length is not precisely known, one can express both the multitude of fields and the cut-off in an effective constant prefactor η of order 1, and write equation (4.3) as εvac=−ℏη12π2c Δℓp2. The energy density ε vac contributes to the right-hand side of the cosmic evolution equation (4.2) with (8/9 π ) η Δ.…”

Localization for Dirac fermions

“…Then, the extension of the 1 dimensional treatment presented here to the more realistic 3 dimensional problem simply follows from adding the angular part of the problem (including the spin) and adapting the treatment of the spatial part given by us to the radial component. Our treatment also seems suitable to further generalizations dealing with higher spin fields, where a unified treatment of bag like BC were recently developed, [29], and applied to the study of the Casimir effect, [30]. Now, we construct the orthonormal stationary modes in our cavity, i.e., we solve the eigenproblem for the Dirac hamiltonian (4) in the domain:…”

The Horava–Lifshitz modifications of the Casimir effect at finite temperature revisited

“…Much a e-mail: hbcheng@ecust.edu.cn (corresponding author) effort has been devoted to the problems and related topics. The Casimir force can be changed by the geometry of the boundaries [16][17][18][19]. The presence of extra dimensions with their size and shape also affect the Casimir effect [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”