Bibliographic record
Abstract
RenormalizationRelativistic quantum field theories generally display infinities at sufficiently high order in a loop expansion.These infinities must first be regulated, meaning that cutoffs are applied to yield finite results that can be manipulated with some mathematical rigor.The results are then renormalized, so that the parameters of the Lagrangian and the cutoffs are eliminated in favor of physical observables such as electric charge and mass.If there are only a finite number of cutoffs as the number of loops increases, the theory is said to be renormalizable and the cutoffs can always be eliminated in favor of a finite number of observables.If the number of required cutoffs increases without bound as the number of loops increases then the theory is said to be nonrenormalizable and one must specify an infinite number of observables to define the theory.The general opinion is that a fundamental theory of nature should be renormalizable.This is based on the belief that there are only a finite number of independent parameters in our universe.An effective theory only needs to describe nature over a finite range of distances or momenta, and such a theory need not be renormalizable.In this chapter we consider the basic aspects of a renormalizable theory and its implications for finite temperatures.For definiteness we study a scalar field theory; the same principles apply to more complicated theories, such as the gauge theories to be studied in later chapters.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.612 | 0.436 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".