Zwiebach 210 Hmwk: Commutator not Equal 0

  • Thread starter Thread starter ehrenfest
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the claim made by Zwiebach regarding the commutator in equation 12.12, specifically that differentiating it with respect to tau yields a commutator that equals zero. The participant argues that this assertion is incorrect, emphasizing that applying the product rule reveals inconsistencies in the calculations. The participant suggests that utilizing equation 12.21 alongside equation 12.1 is necessary to properly analyze the leftmost part of the equation.

PREREQUISITES
  • Understanding of commutators in quantum mechanics
  • Familiarity with Zwiebach's "A First Course in String Theory" and its equations
  • Knowledge of differentiation techniques in mathematical physics
  • Proficiency in applying the product rule in calculus
NEXT STEPS
  • Review the derivation of equation 12.12 in Zwiebach's text
  • Study the implications of equation 12.21 in the context of string theory
  • Explore the application of the product rule in quantum mechanics
  • Investigate the role of differentiation in commutator calculations
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying string theory, as well as educators and researchers interested in the mathematical foundations of quantum mechanics.

ehrenfest
Messages
2,001
Reaction score
1

Homework Statement


Zwiebach claims that differentiating 12.12, which is

X^I (\tau, \sigma) X^J(\tau, \sigma')-X^J(\tau, \sigma') X^I(\tau, \sigma) = 0

w.r.t. tau gives the same commutator with everything dotted. I think that is downright wrong. If you use the product rule to write everything out, it just doesn't work out.


Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
Apply equation (12.21) to the second equation in the first line of equations (12.12).
 
You also have to use 12.1 to get the leftmost part, don't you?
 

Similar threads

Replies
12
Views
3K
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
8K
Replies
1
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K