Discussion Overview
The discussion revolves around the concept of non-renormalizability in the context of pure gravity, particularly focusing on the implications of divergent contributions at higher loop levels and the challenges in making predictions within such a framework. Participants explore theoretical methods, such as the BPHZ method, and the nature of counter terms required for addressing divergences.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant expresses confusion about non-renormalizability, noting that the BPHZ method seems to allow for the subtraction of divergences at each loop level, suggesting that only a finite number of counter terms should be needed.
- Another participant argues that requiring an infinite number of independent terms indicates an infinite number of degrees of freedom, which complicates making useful predictions.
- A different viewpoint suggests that one could use an 'ansatz' for the infinite quantities or approximate divergent integrals with divergent series, potentially leading to finite values through resummation methods.
- Concerns are raised about the need to fix arbitrary finite pieces when introducing new interactions to address divergences, implying that this requirement diminishes predictive power and necessitates additional measurements.
- Some participants propose treating the theory as an effective field theory, noting that the dimensionful nature of Newton's constant suggests limitations in the applicability of gravity at high energy scales.
Areas of Agreement / Disagreement
Participants express differing views on the implications of non-renormalizability and the utility of effective field theories. There is no consensus on the best approach to handle divergences or the predictive power of the theory.
Contextual Notes
Participants highlight the complexity of addressing divergences and the dependence on energy scales, with some suggesting that only a finite number of divergences may be relevant at low energies, while others emphasize the challenges posed by infinite terms at higher energies.