Imaginary-Time Periodicity in ŋ-ξ Spacetime

The relations between the imaginary-time periodicity and the thermal Bogoliubov transformation in ŋ-ξ field theory are discussed. It has been shown that the thermal Bogoliubov transformation leads to the imaginary- time periodicity of the Green function in ŋ-ξ spacetime and to the KMS condition.