Differentiating the complex scalar field

Click For Summary
The discussion revolves around the differentiation of complex scalar fields in the context of Lagrangian mechanics. Participants express confusion over the proper treatment of complex fields, particularly in calculating derivatives with respect to both the field and its complex conjugate. A key point is the realization that treating the scalar field as a complex function leads to incorrect results due to improper application of the chain rule. Clarifications are made regarding the independence of variables and the correct approach to functional derivatives, emphasizing that the relationship between a field and its conjugate must be respected. Ultimately, the conversation highlights the nuances of handling complex variables in theoretical physics, particularly in scalar field theory.
  • #61
Avodyne said:
I don't see the problem ... Is it because of the absolute-value signs?

Yes. The absolute value is not an analytic function. i.e., you can't expand it into a power series.
 

Similar threads

I Scaling Dimension of a Field in CFT
  • · Replies 0 ·
Replies
0
Views
1K
A How was the symmetry used here? ("QFT and the SM" by Schwartz)
  • · Replies 5 ·
Replies
5
Views
1K
A Understanding Hermiticity of Actions in QFT for Checking and Confirming
  • · Replies 4 ·
Replies
4
Views
2K
A What is the meaning of "excess" Goldstone bosons?
  • · Replies 3 ·
Replies
3
Views
2K
I Noether currents for a complex scalar field and a Fermion field
  • · Replies 3 ·
Replies
3
Views
2K
A Effective Action for Scalar and Fermion Fields
  • · Replies 4 ·
Replies
4
Views
2K
A How Do Feynman Diagrams Work in Phi^4 Theory?
  • · Replies 1 ·
Replies
1
Views
2K
I Mass Dimension of Fields (Momentum space)
  • · Replies 2 ·
Replies
2
Views
2K
I The box notation and Lagrangians in field theory
  • · Replies 5 ·
Replies
5
Views
3K
A Lagrangian in the Path Integral
  • · Replies 13 ·
Replies
13
Views
2K