Perturbation theory and total derivatives

Click For Summary
SUMMARY

Total derivatives in the Lagrangian do not contribute in perturbation theory due to their nature of not affecting the equations of motion at leading order. However, they gain significance in non-perturbative regimes, particularly in the context of instantons and differential forms. The discussion highlights the need for deeper exploration into the relationship between total derivatives and homotopy classes, especially in the study of axions.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with perturbation theory in quantum field theory
  • Knowledge of instantons and their role in non-perturbative physics
  • Basic concepts of differential forms and homotopy classes
NEXT STEPS
  • Research the role of instantons in quantum field theory
  • Study the implications of total derivatives in non-perturbative regimes
  • Explore advanced texts on differential forms in physics
  • Investigate the connection between total derivatives and homotopy classes
USEFUL FOR

Quantum field theorists, researchers in theoretical physics, and students studying non-perturbative phenomena in field theories.

ansgar
Messages
514
Reaction score
1
Hi

I was just reading about that total derivatives in the Lagrangian does not give any contributions in perturbation theory but that they can play role in non perturbative regimes.

But there was no statement WHY that is so?

Does anyone have an idea and reading advices? I have the most Quantum field theory books and have tried to search for an answer but can't find anything of value :/

cheers
 
Physics news on Phys.org
I don't know for sure, but I bet the non perturbative relevance of the total derivative has something to do with instantons. Total derivative, differential forms, homotopy classes... there will be some connection there !
 
that is why I am asking, I am doing work on the axion ;)

now I wanted to know why we can forget bout total derivatives in pertruation theory
 

Similar threads

Graduate QFT with vanishing vacuum expectation value and perturbation theory
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why is m_j not a good quantum number in strong-field Zeeman effect?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How are good quantum numbers related to perturbation theory?
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Perturbation lines for the 1s hydrogen electron
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Confusion about Scattering in Quantum Electrodynamics
  • · Replies 134 ·
5
Replies
134
Views
12K
Graduate TD perturbation - state initially in continuous part
  • · Replies 49 ·
2
Replies
49
Views
5K
Insights Introduction to Perturbative Quantum Field Theory - Comments
  • · Replies 108 ·
4
Replies
108
Views
18K
Graduate Time dependent perturbation theory applied to energy levels
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Degenerate perturbation theory -- Sakurai
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Fine structure constant and perturbation theory
  • · Replies 1 ·
Replies
1
Views
2K