Differentiating the complex scalar field

Click For Summary
SUMMARY

The discussion centers on the differentiation of complex scalar fields in the context of Lagrangian density, specifically the equation L = -1/2 (∂μφ ∂μφ* + m²φφ*). Participants clarify the correct approach to functional derivatives, emphasizing the importance of treating φ and φ* as independent variables. The confusion arises from the incorrect application of the chain rule, leading to erroneous results such as ∂/∂φ φ = 2. The correct differentiation involves recognizing the relationship between real and imaginary components of the complex field.

PREREQUISITES
  • Understanding of Lagrangian density in field theory
  • Familiarity with complex functions and their derivatives
  • Knowledge of the Euler-Lagrange equations
  • Basic principles of functional derivatives
NEXT STEPS
  • Study the derivation of Euler-Lagrange equations for complex fields
  • Learn about functional derivatives in the context of field theory
  • Explore the treatment of complex variables in calculus
  • Investigate the implications of treating φ and φ* as independent variables
USEFUL FOR

Physicists, particularly those working in theoretical physics and field theory, as well as students seeking to deepen their understanding of complex scalar fields and Lagrangian mechanics.

  • #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

Undergrad Scaling Dimension of a Field in CFT
  • · Replies 0 ·
Replies
0
Views
1K
Graduate How was the symmetry used here? ("QFT and the SM" by Schwartz)
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Noether currents for a complex scalar field and a Fermion field
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Understanding Hermiticity of Actions in QFT for Checking and Confirming
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Effective Action for Scalar and Fermion Fields
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What is the meaning of "excess" Goldstone bosons?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Classical equivalent of scalar free field in QFT
  • · Replies 5 ·
Replies
5
Views
2K
Graduate How Do Feynman Diagrams Work in Phi^4 Theory?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Scalar decay to one-loop in Yukawa interaction
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Lagrangian in the Path Integral
  • · Replies 13 ·
Replies
13
Views
2K