Week 1 (2/5): No meeting

​

Week 2 (9/5): Spacetime state realism in QFT​​​​​

​

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)

​

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)

​

Epstein-Glaser renormalisation and regularisation (weeks 3-8)

​

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)

​

This involves a bunch of super philosophically-interesting mathematical ideas. I have separated out background by topic:

​

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.)

​

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)

​

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.)

​

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)

​

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)

​

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)

​

This talk by Michael Miller (https://youtu.be/pIiDyAE2Yc8)

​

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)

​

Provisional schedule:

 

Week 3 (16/5) and week 4 (23/5):

​

Fewster and Verch (2015)

Khavkine and Moretti (2015)

 

Week 5 (30/5): No meeting (for New Directions)

 

​Week 6 (6/6): 

​

Holland and Wald (2001, 2002)

Miller's talk

 

Week 7 (13/6): 

​

Khavkine and Moretti (2016), sections 1-2

Kolar et al. (1993), sections 14, 19, 24, 27, 33

​

Background:

Saunders (1989)

Kolar et al. (1993), chapters 3-4

Geroch (1998), sections 5-6

March and Weatherall (2025)

Weatherall and March (2025)

 

Week 8 (20/6): 

 

Khavkine and Moretti (2016), sections 3-4

Aste et al. (2009)​