Computation of the effective action (Peskin 11.4)

In summary, the effective action in Peskin 11.4 is a mathematical quantity used to describe the collective behavior of a system of particles or fields. It is calculated using the path integral formalism and is important for making predictions about the behavior of particles at different energy scales. In quantum field theory, the effective action plays a central role in describing interactions between particles. However, there are limitations to its computation as it may only be applicable to certain types of systems and is an approximation that may not accurately describe the behavior of a system at all energy scales.
  • #1
babamarysol
12
0
The generating functional Z[J] depends on [tex]\phi_{cl}[/tex] trough its dependence on J. At the lowest order in perturbation theory the relation between J(x) and [tex]\phi_{cl}[/tex] is just the classical field equation:

[tex] \left(\frac{\delta L}{\delta \phi}\right)_{\phi=\phi_{cl}} + J(x) = 0 [/tex]

The question is simple: why this expression for the field equation?

Please help me
 
Physics news on Phys.org
  • #2
Ah that's ok it's a functional derivative...
 

1. What is the effective action in Peskin 11.4?

The effective action is a mathematical quantity that describes the collective behavior of a system of particles or fields. In Peskin 11.4, it refers to the quantum field theory effective action, which is used to calculate the interactions between particles in a quantum field theory framework.

2. How is the effective action calculated in Peskin 11.4?

In Peskin 11.4, the effective action is calculated using the path integral formalism. This involves summing over all possible paths of particles in a given field configuration and taking into account the interactions between these particles.

3. Why is the computation of the effective action important?

The computation of the effective action is important because it allows us to make predictions about the behavior of a system of particles or fields. By calculating the effective action, we can determine the strength of interactions between particles and make predictions about their behavior at different energy scales.

4. What is the role of the effective action in quantum field theory?

In quantum field theory, the effective action plays a central role in describing the interactions between particles. It is used to calculate scattering amplitudes, decay rates, and other important physical quantities.

5. Are there any limitations to the computation of the effective action in Peskin 11.4?

Yes, there are limitations to the computation of the effective action in Peskin 11.4. The path integral formalism used to calculate the effective action is only applicable to certain types of systems, and it can become mathematically complex for more complicated systems. Additionally, the effective action is an approximation and may not accurately describe the behavior of a system at all energy scales.

Similar threads

A Effective Action for Scalar and Fermion Fields
    • Quantum Physics
Replies
4
Views
867
I Ricci tensor from this action
    • Special and General Relativity
Replies
4
Views
281
A Lagrangian in the Path Integral
    • Quantum Physics
Replies
13
Views
755
A Complete characterization of local monomials
    • Quantum Physics
Replies
1
Views
544
I Understanding how to derive the Feynman rules out of the path integral
    • Quantum Physics
Replies
33
Views
3K
A Solving this non-holonomic system using Dirac-Bergmann theory
    • Classical Physics
Replies
4
Views
1K
A Is the Higgs Field Responsible for Microscopic Gravitational Effects?
    • Quantum Physics
Replies
24
Views
2K
Differentiation of functional integral (Blundell Quantum field theory)
    • Advanced Physics Homework Help
Replies
1
Views
804
A Scalar Fields with the Same Mass
    • Quantum Physics
Replies
2
Views
1K
A How to find the gamma function for a fermion vacuum energy calculation?
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top