2020/09/30 by M. Sasanpour, C. Ajilyan, Chonoor Ajilyan +1 · 4 citations
Mathematics · Physics and Astronomy · #Analytic continuation #Casimir effect #Casimir pressure #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Helmholtz free energy #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Theoretical physics #Thermodynamics #Zero-point energy #hep-th
paper · pdf · doi:10.1088/1751-8121/ac48ef
published in Journal of Physics A Mathematical and Theoretical 55(12), 125401 (Institute of Physics) · 57 pages, 11 figures, A minor correction
openalex publication_date 2022/01/06 · arxiv created 2022/03/13 · arxiv updated 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.