Exercises for Spontaneous symmetry breaking and field-theory II Prof. Dr. A. Muramatsu
SS 14 Set 5
Exercise 8: Loop expansion for the φ3-theory (10 points) The action for theφ3-theory in d-dimensions is given by
S= Z
ddr 1
2(∇φ)2+1
2m20φ2+ λ 3!φ3
(1)
i) Find the critical dimension of the theory.
ii) Specify the relevant vertex functions to deal with the critical properties.
iii) Find all diagrams that contribute to the relevant vertex functions up to two loop order.
iv) Write down the explicit expression for the diagrams contributing to the relevant vertex functions up to one loop order.
1
