Deriving Srednicki eqn. (9.19)

  • Context: Graduate 
  • Thread starter Thread starter omephy
  • Start date Start date
  • Tags Tags
    deriving Srednicki
Click For Summary
SUMMARY

The discussion focuses on deriving equation (9.19) from Srednicki's "Quantum Field Theory" (QFT) book, specifically within the context of \phi^3 theory. The derivation involves understanding the diagrammatic representations of equations 9.12 and 9.3, which differ significantly from those in \phi^4 theory. Key steps include introducing a counterterm in the Lagrangian, modifying equation 9.10 to incorporate an additional exponential term, and adjusting coefficients in the integral. This process leads to an expansion similar to that in equation 9.11, resulting in three sums instead of two.

PREREQUISITES
  • Understanding of \phi^3 theory in Quantum Field Theory
  • Familiarity with diagrammatic representations in QFT
  • Knowledge of Lagrangian mechanics and counterterms
  • Ability to manipulate integrals and exponential functions in theoretical physics
NEXT STEPS
  • Study the derivation of counterterms in Quantum Field Theory
  • Learn about diagrammatic techniques in \phi^3 theory
  • Review Srednicki's equations 9.10 and 9.11 for deeper insights
  • Explore the differences between \phi^3 and \phi^4 theories in QFT
USEFUL FOR

This discussion is beneficial for theoretical physicists, graduate students studying Quantum Field Theory, and anyone interested in the mathematical foundations of \phi^3 theory and its applications.

omephy
Messages
17
Reaction score
0
can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?
 
Physics news on Phys.org
omephy said:
can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?
Yes -- but to be polite, you should adhere to the guidelines of the homework forums when asking questions like this.
 
It is not a homework problem. Srednicki uses \phi^3 theory and therefore its diagrammatic representation is quite different from the books written in \phi^4 theory. so, I can't even consult other books to derive that equation or to understand the underlying concept. So, I have asked for help.
 
So 9.19 is the sum of the first diagram in Figure 9.12 and Figure 9.3. Now if you want to derive the diagrams in Figure 9.12 from scratch you need to introduce the counterterm (This isn't necessary in \phi^4, so maybe this is where the confusion lies) in the Lagrangian. When you do this you have to rewrite 9.10 to include another exponential (due to the counterterm) which will have (\frac{1}{i}\frac{\delta}{\delta J(x)}) in the integral. You'll also have to change the coefficients in front of the integral in the exponential. Then you can expand like Srednicki does in 9.11, but now you'll have three sums instead of two.
 

Similar threads

Graduate Metastable vacuum and tunneling
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Prefactor in Canonical Quantization of Scalar Field
  • · Replies 4 ·
Replies
4
Views
1K
Graduate What are some example Feynman diagrams in Yang-Mills theory?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Don't understand equation with overleftrightarrow symbol
  • · Replies 10 ·
Replies
10
Views
1K
Graduate Srednicki 58: EM current conservation & Gauge Symmetry
  • · Replies 2 ·
Replies
2
Views
5K
Graduate What are the disconnected Feynman diagrams in QFT?
  • · Replies 3 ·
Replies
3
Views
4K
Quantum Srednicki QFT draft vs printed versions
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Number of particles in the universe
  • · Replies 22 ·
Replies
22
Views
4K
Graduate Sign of Levi-Civita Symbol in spherical coordinates
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Geometry Topology and Physics: Nakahara, Chapt. 1: Weyl Ordering
  • · Replies 1 ·
Replies
1
Views
1K