Discussion Overview
The discussion centers on the role of the ultraviolet (UV) cutoff in quantum chromodynamics (QCD) and whether it is a fundamental aspect of the theory or merely an auxiliary tool. Participants explore various perspectives on the necessity and implications of the cutoff in the context of QFT, particularly in relation to renormalization and the physical scale ##\Lambda_{\rm QCD##.
Discussion Character
- Debate/contested
- Technical explanation
- Mathematical reasoning
Main Points Raised
- Some participants argue that QFT of the Standard Model should be viewed as a continuous theory, with the UV cutoff being an auxiliary tool that should be taken to infinity.
- Others contend that the UV cutoff is a fundamental finite parameter, particularly in QCD, as evidenced by its relationship with ##\Lambda_{\rm QCD}##.
- One participant references Tong's lectures, suggesting that quantum field theories are defined by both their classical action and the cutoff, which is essential for the theory.
- Another viewpoint posits that perturbative formulations of renormalized QCD do not require a cutoff and remain Poincare covariant, highlighting modern treatments like causal perturbation theory and dimensional regularization.
- Concerns are raised about the rigor of dimensional regularization, with some participants noting it uses nonphysical dimensions to handle infinities.
- Asymptotic freedom is mentioned as a reason why QCD might not need a UV cutoff, though this remains an open question.
- Participants discuss the implications of lattice methods versus covariant methods, noting that they may yield different predictions applicable to different regimes.
- There is a call for clarification on whether the predictions from lattice and covariant methods can be tested against the same experiments.
Areas of Agreement / Disagreement
Participants express differing views on the necessity and role of the UV cutoff in QCD, with no consensus reached on whether it is fundamental or merely an auxiliary parameter. The discussion remains unresolved regarding the implications of these differing perspectives.
Contextual Notes
Some participants note that the existence of a mathematically rigorous formulation of the full theory of QCD is still an open question, and the discussion touches on the limitations of various regularization methods.