Finite temperature Casimir effect for massive scalars in a magnetic field

Abstract

The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass, and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.

13 pages, RevTeX4. arXiv admin note: text overlap with arXiv:1304.6417

References in corpus (5)

• Casimir force on a piston
• Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
• Multiple Scattering Methods in Casimir Calculations
• Zeta Function Methods and Quantum Fluctuations
• Effective Electromagnetic Lagrangian at Finite Temperature and Density in the Electroweak Model

Cited by in corpus (6)

• Casimir effect of a Lorentz-violating scalar in magnetic field
• Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field
• Magnetic field corrections to the repulsive Casimir effect at finite temperature
• Casimir effect in magnetic dual chiral density waves
• Anomalous-magnetic-moment-enhanced Casimir effect
• Quantum Vacuum Fluctuations in a Chromomagnetic-like Background