The classroom distribution for the forthcoming days is the following:

Monday 6/11
Lecture 1: classroom AP003 from 11:00 to 13:00 hrs.
Lecture 2: classroom AP003 from 15:00 to 17:00 hrs.

Wednesday 8/11
Lecture 3: classroom AP302 from 11:00 to 13:00 hrs.
Lecture 4: classroom AP302 from 15:00 to 17:00 hrs.

Monday 13/11
Lecture 5: classroom AP201 from 11:00 to 13:00 hrs.
Lecture 6: classroom AP302 from 15:00 to 17:00 hrs.

Wednesday 15/11
Lecture 7: classroom AP302 from 11:00 to 13:00 hrs.
Lecture 8: classroom AP302 from 15:00 to 17:00 hrs.

Outline

The lectures will develop a pedagogical introduction to the asymptotic structure of gauge theories and gravity. A systematic derivation of the asymptotic symmetries will be given, with a particular emphasis on the asymptotically flat case.  Hamiltonian methods at spatial infinity will be followed throughout. Matching with null infinity will also be discussed.

Contents

1. Hamiltonian vector fields and Hamiltonian functions
    Proper and improper gauge transformations
    General theorems

2. Asymptotic structure of Chern-Simons theories with multiple boundaries

3. Connection between spatial infinity and null infinity in (asymptotically) Minkowski space: the example of the scalar field

4. Asymptotic symmetries of electromagnetism and angle-dependent u(1) transformations

5. Gravity in the asymptotically flat case – BMS group

6. Supertranslation ambiguity in the angular momentum; nonlinear redefinitions leading to a supertranslation invariant angular momentum

7. Further topics (depending on time): higher dimensions, supergravity

References

• Symplectic form with surface term contribution, electromagnetism
  – M. Henneaux, C. Troessaert – “Asymptotic symmetries of electromagnetism at spatial infinity” – JHEP 05 (2018) 137- arXiv
• Connection between spatial infinity and null infinity (scalar field)
  – M. Henneaux, C. Troessaert –”Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity” – JHEP 05 (2019) 147 – arXiv
  + enclosed slides
• BMS group in Hamiltonian form
  – M. Henneaux, C. Troessaert – “The Asymptotic Structure of Gravity at Spatial Infinity in Four Spacetime Dimensions” – Proceedings of the Steklov Institute of Mathematics 309 (2020) 127–149 (available on the arXiv)
  – M. Henneaux, C. Troessaert –”Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity” – JHEP 07 (2018) 171 – arXiv
  (see also earlier work M. Henneaux, C. Troessaert – “BMS group at spatial infinity: the Hamiltonian (ADM) approach” – JHEP 03 (2018) 147 – arXiv)
• Supertranslation-invariant Lorentz generators
  – O. Fuentealba, M. Henneaux and C. Troessaert – « Logarithmic supertranslations and supertranslation-invariant Lorentz charges » – JHEP 02 (2023) 248- arXiv
  – O. Fuentealba, M. Henneaux and C. Troessaert – « Asymptotic Symmetry Algebra of Einstein Gravity and Lorentz Generators » – Phys. Rev. Lett. 131 (2023) 111402 – arXiv
  (for electromagnetism: O. Fuentealba, M. Henneaux and C. Troessaert – « A note on the asymptotic symmetries of electromagnetism » – JHEP 03 (2023) 073 – arXiv)

Resources

• Lectures PDF