Fractional derivative quantum fields at positive temperature

This paper considers fractional generalization of finite temperature Klein–Gordon (KG) field and vector potential in covariant gauge and static temporal gauge. Fractional derivative quantum field at positive temperature can be regarded as a collection of infinite number of fractional thermal oscillators. Generalized Riemann zeta function regularization and heat kernel techniques are used to obtain the high temperature expansion of free energy associated with the fractional KG field. We also show that quantization of the fractional derivative fields can be carried out by using the Parisi–Wu stochastic quantization.