Abstract
The Lorentz and $CPT$ symmetries are not violated at the highest laboratory energies available. However these symmetries may be violated at Planck scale. A particular development is to investigate the breakdown of Lorentz and $CPT$ symmetries by introducing an aether field that exhibits nonzero vacuum expectation value along the fifth dimension. The interactions of the aether field with scalar, electromagnetic, and fermions fields are analyzed. The Stefan-Boltzmann law and Casimir effect at finite temperature are calculated using the Thermo Field Dynamics formalism.
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