Casimir free energy for massive fermions: a comparative study of various approaches

Abstract

We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield in general different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

“…Using Eqs. (4,5,11), for the case of TL/Lv s Lorentz violating massive scalar field the zero-order Casimir energy density is converted to:…”

“…Casimir's seminal prediction of the Casimir effect, made over 60 years ago, set the stage for extensive research in this field [1]. The Casimir effect, which arises from distortions in the vacuum, has been the subject of thorough investigation over the years, with notable contributions from various works [2][3][4]. Such distortions in the vacuum can be induced by the presence of boundaries in the space-time or by external factors such as gravity.…”