ELEANOR MARCH
​(pt)QFT reading group
The philosophical topics in QFT reading group (started by myself and James Read in Hilary term 2025) will be continuing this Trinity term. We'll be meeting on a Friday at 16:00 UK time. There will also be an option to join online.
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A provisional schedule of topics and readings for the current term is below (subject to change). There is some expectation to do some of the reading in advance, but the aim of this group is to develop (collective) understanding - so if you just want to focus on one item/sub-topic or get stuck on something, that's totally fine and you'll probably be helping the rest of us out! Everyone is welcome to suggest topics, readings, or to present if they would like - get in touch with me or James.​​​ A provisional schedule of topics for future terms is at the bottom of this page.
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Trinity term 2025
Week 1 (2/5): No meeting
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Week 2 (9/5): Spacetime state realism in QFT​​​​​
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Noel Swanson (2020) - "How to Be a Relativistic Spacetime State Realist" (The British Journal for the Philosophy of Science 71 (3): pp. 933-957. doi: 10.1093/bjps/axy041)
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Background:
David Wallace and Christopher G. Timpson (2010) - "Quantum Mechanics on Spacetime I: Spacetime State Realism" (The British Journal for the Philosophy of Science 61 (4): pp. 697-727. doi: 10.1093/bjps/axq010)
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Epstein-Glaser renormalisation and regularisation (weeks 3-8)
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The aim is to understand this paper:
Igor Khavkine and Valter Moretti (2016) - "Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT" (Communications in Mathematical Physics 344: pp. 581-620. doi: 10.1007/s00220-016-2618-7)
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This involves a bunch of super philosophically-interesting mathematical ideas. I have separated out background by topic:
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Jet bundles:
D. J. Saunders (1989) - The Geometry of Jet Bundles, especially chapters 4, 6 (Cambridge: CUP. doi: 10.1017/CBO9780511526411)
Ivan Kolar et al. (1993) - Natural Operations in Differential Geometry, chapters 3-4 (New York: Springer-Verlag. doi: 10.1007/978-3-662-02950-3.)
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Natural bundles (including "background" and "dependence"):
Ivan Kolar et al. (1993) - Natural Operations in Differential Geometry, chapter 4 (New York: Springer-Verlag. doi: 10.1007/978-3-662-02950-3.)
Robert Geroch (1996) - "Partial Differential Equations of Physics" (doi: 10.48550/arXiv.gr-qc/9602055)
Eleanor March and James Owen Weatherall (2025) - "A Puzzle About General Covariance and Gauge" (doi: 10.48550/arXiv.2405.03906)
James Owen Weatherall and Eleanor March (2025) - "Natural Theories" (doi: 10.48550/arXiv.2504.05703)
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The non-linear Peetre theorem:
Ivan Kolar et al. (1993) - Natural Operations in Differential Geometry, chapter 5 (New York: Springer-Verlag. doi: 10.1007/978-3-662-02950-3.)
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Locally-covariant QFT:
Christopher J. Fewster and Rainer Verch (2015) - "Algebraic Quantum Field Theory in Curved Spacetimes" (In: Brunetti, R., Dappiaggi, C., Fredenhagen, K., Yngvason, J. (eds.) Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer, Cham. doi: 10.1007/978-3-319-21353-8_4)
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Igor Khavkine and Valter Moretti (2015) - "Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction" (In: Brunetti, R., Dappiaggi, C., Fredenhagen, K., Yngvason, J. (eds.) Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer, Cham. doi: 10.1007/978-3-319-21353-8_5)
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Wavefront sets:
Rainer Verch (1999) - "Wavefront Sets in Algebraic Quantum Field Theory" Communications in Mathematical Physics 205, pp. 337-367. (doi: 10.1007/s002200050680)
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Epstein-Glaser renormalisation in locally-covariant QFT:​
Stefan Hollands and Robert M. Wald (2001) - "Local Wick polynomials and time ordered products of quantum fields in curved spacetime" (Communications in Mathematical Physics 223: pp. 289-326. doi: 10.1007/s002200100540)
Stefan Hollands and Robert M. Wald (2002) - "Existence of local covariant time ordered products of quantum fields in curved spacetime". (Communications in Mathematical Physics 231: pp. 309-345. doi: 10.1007/s00220-002 0719-y)
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Romeo Brunetti and Klaus Fredenhagen (2000) - "Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds" (Communications in Mathematical Physics 208 (3): pp. 623-661. doi: 10.1007/s002200050004.)
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This talk by Michael Miller (https://youtu.be/pIiDyAE2Yc8)
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Regularization in locally-covariant QFT:
Andreas Aste et al. (2010) - "Regularization in quantum field theory from the causal point of view" (Progress in Particle and Nuclear Physics 64 (1): pp. 61-119. doi: 10.1016/j.ppnp.2009.08.003)
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Provisional schedule:
Week 3 (16/5) and week 4 (23/5):
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Fewster and Verch (2015) - sections 4.1-3; 4.5.1-3; 4.9.1
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Background:
March and Weatherall (2025)
Week 5 (30/5): No meeting (for New Directions)
​Week 6 (6/6):
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Verch (1999)
Fewster and Verch (2015) - section 4.5.4
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Optional:
Khavkine and Moretti (2015)
Week 7 (13/6):
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Hollands and Wald (2001)
Khavkine and Moretti (2016) - section 3
Week 8 (20/6):
Miller's talk​
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Optional:
Brunetti and Fredenhagen (2000)
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Topic schedule for future terms
Michaelmas/Fall/Autumn 2025 (Sep. 26th-Dec. 12th): Topics at the intersection of QFT and black holes
Hilary/Winter 2026 (Jan. 2nd-March 20th): Lagrangian QFT (proper)
Trinity/Spring 2026 (April 10th-June 26th): Energy conditions in QFT
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Seiberg-Witten theory
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BV/BFV formalism
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Measurement in QFT
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Spectrum conditions and the duality condition in QFT
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Locality and non-locality in QFT
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Causality in QFT