The Mathematics of Quantum Field Theory
a learning seminar
by
John Huerta and Gonçalo Oliveira
Practical information
What is this?
This year (Spring and Summer
2024), John Huerta
and Gonçalo
Oliveira are running a learning seminar on the mathematics of quantum field
theory. We started on March 18th, and will continue into July until we're
tired of it!
The seminar consists of two tracks:
- Gonçalo is discussing constructive quantum field theory, leading up to the construction of interacting scalar field theories in two-dimensions.
- John is discussing the Batalin–Vilkovisky (BV) formalism, leading up to the perturbative quantization of Yang–Mills theory in 4-dimensions.
Where and when?
We normally meet on Mondays and Wednesdays at 1 PM - 3 PM, in room 4.35 of the mathematics building at Instituto Superior Técnico. However, we often change our schedule on a whim. If you are local to Lisbon and would like to be part of this, please email me.
The BV Track
Notes
You can see our in-progress notes here: (Draft version! Use with care!!)- Notes for the BV track by Rui Peixoto and Björn Gohla, from talks by John Huerta unless noted otherwise.
Upcoming talks
The following is a tentative schedule of upcoming speakers in the BV track and their topics. The dates are subject to change, which will be announced by email.
-
20 May: John Huerta on errata, Rui Peixoto on the finite-dimensional quantum BV formalism (part two). -
27 May: Manuel Araújo on finite-dimensional Feynman diagrams. -
3 June: Manuel Araújo on finite-dimensional Feynman diagrams (part two). -
5 June: Roger Picken on the Wilsonian definition of a scalar QFT. -
10 June: Holiday, no seminar. -
12 June: Leander Stecker on elliptic complexes, gauge fixing operators, and the propagator. -
17 June: Leander Stecker on elliptic complexes, gauge fixing operators, and the propagator (part two). -
24 June - 10 July: No seminar. -
17 July: John Huerta on perturbative quantization (part one). -
24 July: John Huerta on perturbative quantization (part two). -
31 July: John Huerta on perturbative quantization (part three). -
5 August: John Huerta on perturbative quantization (part four). -
12 August: John Huerta on heat kernel regularization. -
21 August: John Huerta on BV quantization (part one). -
26 August: John Huerta on BV quantization (part two). -
28 August: John Huerta on BV quantization (part three).
Talks waiting to be scheduled
- Björn Gohla on the simplicial set of quantizations.
- Someone on obstructions to quantization.
- John Huerta on the quantization of Yang–Mills theory.
Older talks
Please refer to the notes!
References
- Kevin Costello, Renormalisation and the Batalin–Vilkovisky formalism, arXiv:0706.1533.
- Kevin Costello, Renormalization and effective field theory, American Mathematical Society, Providence, 2011. Draft version.
- Kevin Costello and Owen Gwilliam, Factorization algebras and quantum field theory, vol 2, Cambridge University Press, Cambridge, 2021. Draft version.
- Chris Elliott, Brian Williams, Philsang Yoo, Asymptotic freedom in the BV formalism, J. Geom. Phys. 123 (2018), 246–283. arXiv:1702.05973.
- Owen Gwilliam, Factorization algebras and free field theories, PhD thesis, Department of Mathematics, Northwestern University, 2012.
- Pavel Mnev, Quantum field theory: Batalin-Vilkovisky formalism and its applications, American Mathematical Society, Providence, 2019. (Based on lecture notes available as arXiv:1707.08096.)
The Constructive Track
Please see
this
page, maintained by Gonçalo.
© John Huerta