Thermodynamics of the Lee-Wick partners: An alternative approach

Abstract

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.

Toy model based analysis on the effect of the Lee-Wick partners in the evolution of the early universe

“…In this work we will mainly focus on the main results of [15,16] where the authors have independently derived the thermodynamic properties of the Lee-Wick resonances at high temperatures; i.e., when the temperature of the fluid containing both the standard model particles and their Lee-Wick partners is much higher than the mass of the heavy Lee-Wick resonances. It is shown that the Lee-Wick fields at high temperature contribute negatively to the energy density and pressure, although the net pressure and energy density which gets contributions from the standard model particles and their Lee-Wick partners remain positive.…”

“…It is shown that the Lee-Wick fields at high temperature contribute negatively to the energy density and pressure, although the net pressure and energy density which gets contributions from the standard model particles and their Lee-Wick partners remain positive. Two different approaches were taken in these two works, [15,16], to derive the thermodynamic properties of Lee-Wick resonances at high temperature. As a functional integral formulation of Lee-Wick theories is not properly derived, the authors of [15] have followed a method of statistical field theory developed in [17] to calculate the thermodynamic properties of these unusual Lee-Wick partners which are treated as unstable resonances.…”

“…As a functional integral formulation of Lee-Wick theories is not properly derived, the authors of [15] have followed a method of statistical field theory developed in [17] to calculate the thermodynamic properties of these unusual Lee-Wick partners which are treated as unstable resonances. On the other hand the authors of [16] work with a variant of Lee-Wick's original idea, first predicted by Boulware and Gross in [18]. In this formulation the unusual Lee-Wick fields, unlike Lee-Wick's initial work, live in a definite metric space but carry negative energy.…”

“…Using these negative energy fields one can reproduce the same thermodynamic properties as in [15] from the first principles of statistical mechanics. Without dealing much with the intricacies of these two methods, we will follow the main results of these two works [15,16]. It is to be noted that although, by assumption, an indefinite metric state cannot be an initial or final state of a scattering process, still they may contribute to the thermodynamics of the system.…”

“…On the other hand, a cosmic fluid infested with Lee-Wick resonances at very high temperatures leads to an unusual equation of state (! ¼ 1) [15,16], which might have affected the evolution of the early universe in an unconventional way. 1 This present article deals with features of such an unconventional cosmological scenario.…”