By Harmen Jakob Warringa
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Extra resources for Thermodynamics of QCD-inspired theories
The 2PI formalism is very useful for out-of-equilibrium quantum field theory calculations (see for example Berges (2005)). This is because unlike the 1PI method, the 2PI formalism lacks the so-called secularity problem, which causes the perturbation series of a time-dependent quantity to diverge at late times (see for example Arrizabalaga (2004)). Moreover, it is very natural to introduce Gaussian initial density matrices in the 2PI formalism. Since in this thesis all results are obtained for equilibrium situations, the 2PI formalism will not be discussed further.
N − 1. 4) where ϑ(x) is the step function. This step function reflects the fact that due the original constraint on the φ fields, πi πi never can be larger than N/g2b . The effective Lagrangian density Leff can be found by inserting the expression for σ in terms of π in the original Lagrangian density. 5) where the term proportional to δ2 (0) arises from integration over the delta function δ(N/g2b − φi φi ). 4. The effective potential 55 For small values of g2b the ϑ(x) function is only vanishing when π(x) is large.
35) is over a complete set of functions that satisfy the periodic boundary conditions in imaginary time for scalar fields. The trace can be evaluated by going to momentum space. 36) P were the sum-integral is defined in Eq. 32). The pressure can now be calculated by applying Eq. 14). Since it is only possible to measure pressure differences, it is convenient to normalize the pressure at zero temperature to zero. 37) P will be subtracted from the contribution at finite temperature which is − 1 2 log(P2 + m2 ) .