Casimir free energy for massive fermions: a comparative study of various approaches
arXiv:2009.03578 · doi:10.1088/1751-8121/ac48ef
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.
arXiv comment57 pages, 11 figures, A minor correction
References in corpus (29)
- New Developments in the Casimir Effect
- Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
- The Casimir effect: Recent controversies and progress
- Measurement of the Temperature Dependence of the Casimir-Polder Force
- Basics of thermal field theory -- a tutorial on perturbative computations
- The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
- Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
- Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action
- Thermal Casimir effect in ideal metal rectangular boxes
- Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes
- Brane Worlds and the Cosmic Coincidence Problem
- Thermal and non-thermal signatures of the Unruh effect in Casimir-Polder forces
- Heavy-Quark Free Energy, Debye Mass, and Spatial String Tension at Finite Temperature in Two Flavor Lattice QCD with Wilson Quark Action
- Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
- Casimir scaling and renormalization of Polyakov loops in large-N gauge theories
- Recent Developments in the Casimir Effect
- Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
- The Casimir energy of a massive fermionic field confined in a d+1 dimensional slab-bag
- Strongly Interacting Fermions and Phases of the Casimir Effect
- Interacting Fermions, Boundaries, and Finite Size Effects
- Finite temperature fermionic condensate and currents in topologically nontrivial spaces
- Thermofield Dynamics and Casimir Effect for Fermions
- Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field
- Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions
- The Casimir effect for parallel plates involving massless Majorana fermions at finite temperature
- Free energy and entropy for thin sheets
- Finite temperature Fermionic Casimir interaction in Anti-de Sitter spacetime
- Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution
- Generalized Schlömilch's formulas and thermal Casimir effect of a fermionic rectangular box