Why some functional integral(in QTF theo)of a product equal product of two the integr

  • Context: Graduate 
  • Thread starter Thread starter ndung200790
  • Start date Start date
  • Tags Tags
    Functional Product
Click For Summary
SUMMARY

The discussion centers on the calculation of functional integrals in Quantum Field Theory (QFT) as presented in chapter 11 of "An Introduction to Quantum Field Theory" by Peskin and Schroeder. Specifically, the participant seeks clarification on why the integral of the product of two exponentials of the exact Lagrangian and the counterterm Lagrangian can be computed separately. The conclusion drawn is that the ability to separate these integrals stems from the properties of the counterterms, which can be freely chosen, allowing for the simplification of the integral calculations as demonstrated in equations (11.57), (11.59), and (11.62).

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT) principles
  • Familiarity with Lagrangian mechanics in the context of QFT
  • Knowledge of functional integrals and their properties
  • Experience with Peskin and Schroeder's "An Introduction to Quantum Field Theory"
NEXT STEPS
  • Study the derivation of functional integrals in QFT, focusing on the separation of exponential terms
  • Review the concepts of counterterms and their role in renormalization
  • Examine the specific equations (11.57), (11.59), and (11.62) in detail for deeper understanding
  • Explore advanced topics in QFT, such as connected diagrams and their contributions to functional integrals
USEFUL FOR

This discussion is beneficial for graduate students in physics, researchers in Quantum Field Theory, and anyone looking to deepen their understanding of functional integrals and Lagrangian formulations in QFT.

ndung200790
Messages
519
Reaction score
0
Please teach me this:
In section 11.4 chapter 11 of QTF theory book of Peskin&Schroeder,computing Effective Action,they calculate a functional integral of product of two exponentials of ''exact'' Lagrangian and ''counterterm'' Lagrangian with the same variable of integral(value of field).I do not understand why they can calculate the integral by integrating separately the two exponentials.Why the integral of the product of two exponentials equals the two integrals of each exponential?(That is (11.57),(11.59),(11.62) chapter 11).
Thank you very much for your kind helping.
 
Physics news on Phys.org


Now,I am thinking that it is possible,because the freely choosing the value of counterterms.Is it correct?
 


Sorry,I had misunderstood the authors,because the product of the two integrals adding connected diagrams is equal the functional integral of product of the two factors.
 

Similar threads

Graduate Orthogonality of variations in Faddev-Popov method for path integral
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Two-point correlation function in path integral formulation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Physical insight into integrating a product of two functions
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Triple Product in Laplace Transform
  • · Replies 2 ·
Replies
2
Views
2K
Partition function of a particle with two harmonic oscillators
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Why should a Fourier transform not be a change of basis?
  • · Replies 43 ·
2
Replies
43
Views
8K
Graduate Can anyone give me the details of creating a cat state in Circuit QED?
  • · Replies 16 ·
Replies
16
Views
4K
Undergrad Why is the Maximum Likelihood Function a product?
  • · Replies 3 ·
Replies
3
Views
2K
Integrating a dot product inside an exponential
  • · Replies 2 ·
Replies
2
Views
7K
Graduate Feeling uncomfortable about Wick-rotations
  • · Replies 18 ·
Replies
18
Views
6K