Analysing topological aspects of QFT within the locally covariant algebraic framework
Bibliographic record
Abstract
The locally covariant approach to quantum field theory (LCQFT) is a manifestly covariant functorial approach to quantum field theory (QFT) that applies to curved spacetimes and which builds on the local algebraic approach. In this thesis we investigate applications of LCQFT to topological aspects of QFT. \n \nWe analyse extensions of quantum field theories defined on contractible globally hyperbolic regions of spacetime, using Fredenhagen's universal algebra construction. This construction involves covering a spacetime by open contractible causally convex subregions, and applying the functor that defines the theory to each of them to get a net of local algebras. The universal algebra is then obtained by taking the colimit of this net. Morphisms between universal algebras can be defined with the result that the mapping between spacetimes and their corresponding universal algebras defines a functor. We prove two main results about this universal construction, which both require considerable geometric apparatus. \n \nFirst we prove that for a broad class of theories modelled on the free scalar/Dirac field, the functor assigning universal algebras satisfies the Einstein causality axiom. We then restrict attention to Fermionic theories in this class, and analyse the universal theories obtained from the subtheories that assign even subalgebras. We show that for each spacetime $\\mathcal{M}$, the universal theory assigns an algebra which decomposes into a product (in the categorical sense) of subalgebras, that are in bijective correspondence with the set $H^{1}(\\mathcal{M},\\mathbb{Z}_2)$. The latter set counts the number of distinct spin structures the spacetime manifold $\\mathcal{M}$ permits. The universal algebra for a Fermionic theory therefore has the geometric information encoded in it necessary to define half integer spin fields.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".