Thermodynamics of the Lee-Wick partners: An alternative approach

It was pointed out some time ago that there can be two variations in which the divergences of a quantum field theory can be tamed using the ideas presented by Lee and Wick. In one variation the Lee-Wick partners of the normal fields live in an indefinite metric Hilbert space but have positive energy and in the other variation the Lee-Wick partners can live in a normal Hilbert space but carry negative energy. Quantum mechanically the two variations mainly differ in the way the fields are quantized. In this article the second variation of Lee and Wick's idea is discussed. Using statistical mechanical methods the energy density, pressure and entropy density of the negative energy Lee-Wick fields have been calculated. The results exactly match with the thermodynamic results of the conventional, positive energy Lee-Wick fields. The result sheds some light on the second variation of Lee-Wick's idea. The result seems to say that the thermodynamics of the theories do not care about the way they are quantized.