Discussion Overview
The discussion revolves around the implications of including higher than second order derivatives in the Lagrangian of quantum field theories (QFT). Participants explore the potential issues that arise from such formulations, particularly concerning the equations of motion (EOM) and the concept of locality.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions the importance of restricting the Lagrangian to at most second order derivatives, asking what physical troubles might arise from higher order EOM.
- Another participant suggests that non-locality is a significant issue, indicating that higher order derivatives could lead to a Taylor series expansion that complicates the theory.
- A different viewpoint states that non-locality specifically arises from negative powers of momentum in the Lagrangian, while a finite series of positive powers remains local.
- There is a query about the mechanism by which negative powers of momentum lead to non-locality and the specific implications of this phenomenon.
- One participant notes that while effective field theories can include higher derivative terms, such theories are not renormalizable and thus are not expected to represent fundamental theories.
Areas of Agreement / Disagreement
Participants express differing views on the implications of higher order derivatives in QFT, particularly regarding locality and renormalizability. There is no consensus on the underlying reasons for avoiding higher order derivatives or the consequences of their inclusion.
Contextual Notes
The discussion highlights the complexity of the relationship between derivative order in Lagrangians and physical implications, such as locality and renormalizability, without resolving the specific mechanisms or definitions involved.
Who May Find This Useful
This discussion may be of interest to those studying quantum field theory, particularly in relation to the formulation of Lagrangians and the implications of derivative orders on physical theories.