• Corpus ID: 73714811

Euclidean Field Theory

@inproceedings{Peeters2011EuclideanFT,
  title={Euclidean Field Theory},
  author={Kasper Peeters and Marija Zamaklar},
  year={2011}
}

• K. Peeters, M. Zamaklar
• Published 2011
• Physics

Summary: The generating functional of a Euclidean quantum field theory in dspace dimensions can alternatively be interpreted as a partition sum in a classicalstatistical model in d dimensions. The corresponding inverse temperature is thenrelated to Planck’s constant by b ˘1/¯h. I See also: Discussions like these can be found in many places, e.g. chapter 2 of thebook by Smit [10] or chapter V.2 of the book by Zee [13]. 1.3. Finite temperature quantum field theory In standard quantum field theory courses one almost always works with systems atvanishing temperature. That is to say, the state which is used to define all correlationfunctions is taken to be the vacuum state j0iof the free theory, with no particles. Thepropagator, for instance, is defined asG F (x y) = h0jT f ˆ(x) f ˆ(y)j0i. (1.9)However, we can certainly also construct a quantum theory of fields in which we usea thermal state instead of the no-particle vacuum. Instead of computing a vacuumexpectation value, we then have to computeG