14 - Field theory at non-zero temperature

Summary

The discussion of the previous chapter has given us some understanding of the effective potential for the standard GSW model. A similar analysis can be performed for any grander unified theory of elementary fields.

However, the pattern of symmetry breaking that we now observe was not always present. Standard cosmology predicts that in the early states of the universe there was a large matter and radiation density at high temperature. On the basis of simple arguments from statistical mechanics we would not expect the symmetries of such a system to be those we experience now.

The existence of different phases may seem of marginal interest, since the cooling down of the universe to what is effectively absolute zero occurred in the distant past. This is not so. The reason is that different field theories for current (zero-temperature) unification will, in general, have different cosmological implications if used to describe the early evolution of the universe. Given that the mass scales introduced by grand unification are much higher than those accessible to accelerator physics, cosmological predictions provide an important means of discrimination between candidate theories.

We shall not attempt early-universe calculations. In this chapter we only consider the first step, the calculation of temperature-dependent quantum effects in field theories at non-zero temperature.