Thermo-field Dynamics of the Casimir Effect and Its Quantum Deformation

The Casimir effect of the deformed cavity field at finite temperature is investigated by generalizing the thermo field dynamics formalism into q-deformed version. It has been shown that the impact of q-deformation on the Casimir force only manifests in the finite temperature case and the expression for the ideal pure vacuum remains unchanged, which just coincides with the suggestions of Man’ko et al. Phys. Lett. A 176(1993 173 about the nature of q-oscillators as the nonlinear vibrations of electromagnetic field.