In comparing different renormalization procedures why do we care about symmetry?

Click For Summary
SUMMARY

This discussion centers on the significance of preserving Lorentz and gauge invariance during renormalization procedures in quantum field theory. It is established that while the final physical results are independent of the chosen renormalization method, the preservation of symmetry during calculations is crucial. Gerard 't Hooft's work confirms that various renormalization procedures yield consistent results, and there exists at least one method that maintains these symmetries throughout the process.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with renormalization techniques
  • Knowledge of Lorentz invariance and gauge invariance
  • Awareness of 't Hooft's contributions to theoretical physics
NEXT STEPS
  • Research different renormalization procedures in quantum field theory
  • Study the implications of Lorentz invariance in physical theories
  • Explore gauge invariance and its role in particle physics
  • Examine 't Hooft's proofs regarding renormalization and symmetry
USEFUL FOR

The discussion is beneficial for theoretical physicists, graduate students in physics, and researchers focusing on quantum field theory and renormalization techniques.

alemsalem
Messages
173
Reaction score
5
Why do we care about Lorentz or gauge invariance if we're going to remove the cutoff at the end. our physical answers are independent of the procedure,, why do we care about preserving the symmetry "during" the calculation?

Thanks for your time!
 
Physics news on Phys.org
In fact we don't care!

The only important thing is that somebody (= 't Hooft) as proved that different procedures give the same results, and there exists a procedure that preserves those symmetries.
So we know that the result has Lorentz and gauge symmetries and you can chose any procedure to make your calculation
 

Similar threads

Undergrad How Do Gauge and Phase Symmetries Differ in Quantum Systems?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Symmetries of particle interacting with external fields (Ballentine)
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Why is gauge symmetry not a true symmetry?
  • · Replies 46 ·
2
Replies
46
Views
8K
Graduate QFT: Understanding Counter-Terms for Renormalization
  • · Replies 6 ·
Replies
6
Views
4K
Graduate What is the significance of the renormalization scale μ?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Calculating group representation matrices from basis vector/function
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Why do we use BRST in Yang Mills and where does it come from?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Why do we know the particle/quantum field theory is phys of symmetries
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Gauge transformations at infinity
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is Poincare symmetry the real thing?
  • · Replies 31 ·
2
Replies
31
Views
4K