Question

Rederive the Ward-Takahashi identity (12.142) using operator methods. One may assume without loss of generality that the $y_1, y_2, . . y_p$ are already time-ordered. One can then write the T-product as a sum of terms with explicit $\theta$-functions enforcing the time-ordering of the current relative to the $\phi_n$ fields, thereby facilitating the application of the spacetime-derivative. The contact terms arise from the $\mu=0$ derivative, which result in a series of equal-time commutators, at which point (12.128) may be employed.

   Rederive the Ward-Takahashi identity (12.142) using operator methods. One may assume without loss of generality that the $y_1, y_2, . . y_p$ are already time-ordered. One can then write the T-product as a sum of terms with explicit $\theta$-functions enforcing the time-ordering of the current relative to the $\phi_n$ fields, thereby facilitating the application of the spacetime-derivative. The contact terms arise from the $\mu=0$ derivative, which result in a series of equal-time commutators, at which point (12.128) may be employed.
 
Show more…
The Conceptual Framework of Quantum Field Theory
The Conceptual Framework of Quantum Field Theory
Anthony Duncan 1st Edition
Chapter 12, Problem 8 ↓

Instant Answer

verified

Step 1

The expression to consider is: \[ T\{ j^\mu(x) \phi_{n_1}(y_1) \phi_{n_2}(y_2) \ldots \phi_{n_p}(y_p) \}. \]  Show more…

Show all steps

lock
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Rederive the Ward-Takahashi identity (12.142) using operator methods. One may assume without loss of generality that the $y_1, y_2, . . y_p$ are already time-ordered. One can then write the T-product as a sum of terms with explicit $\theta$-functions enforcing the time-ordering of the current relative to the $\phi_n$ fields, thereby facilitating the application of the spacetime-derivative. The contact terms arise from the $\mu=0$ derivative, which result in a series of equal-time commutators, at which point (12.128) may be employed.
Close icon
Play audio
Feedback
Powered by NumerAI
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever