Στις 14 & 19 Μαΐου ο Adrien Fiorucci (Ecole Polytechnique, Université Libre de Bruxelles, International Solvay Institutes) θα δώσει σειρά διαλέξεων στην αίθουσα σεμιναρίων του Σπουδαστηρίου (4ος όροφος) πάνω σε επιφανειακά φορτία σε βαρύτητα και θεωρίες βαθμίδας.
Ακολουθεί το πρόγραμμα, η περίληψη των διαλέξεων καθώς και η αντίστοιχη βιβλιογραφία:
Πέμπτη 14 Μαΐου, 12:00 – 14:00
Τρίτη 19 Μαΐου, 12:00 – 14:00
Περίληψη:
These lectures aim to provide an introduction to covariant phase space methods for computing conserved charges in gauge theories, with particular emphasis on gravity. Recent developments will be discussed and illustrated through the computation of gravitational charges and charge algebras in flat and anti-de Sitter spacetimes.
The plan is as follows: (1) the variational bicomplex; (2) symmetries and Noether’s theorems; (3) surface charges from covariant phase space; (4) charge algebra, conservation and integrability.
The first lecture will cover the first two points. After a short historical introduction, we shall introduce the variational bicomplex as the mathematical framework underlying the formulation of Lagrangian field theories. Within this formalism, Noether’s theorems for variational symmetries will be reviewed, and the relation between gauge symmetries and conserved surface charges will be explained. This contrasts with global symmetries, which lead to conserved volume charges. The examples of electrodynamics and Einstein gravity will be discussed.
The second lecture will cover the last two points. We shall construct the covariant phase space, which allows one to calculate surface charges by contracting a symplectic structure, thereby lifting Hamiltonian methods to a covariant setting. The conditions under which these charges are well-defined, conserved or integrable will then be investigated, and their algebra computed. The formalism will be exemplified by discussing surface charges in Einstein gravity, with applications to asymptotically flat and anti-de Sitter spacetimes if time allows.
Lecture notes shall be made available by the end of the term.
Βιβλιογραφία:
Pedagogical resources:
A. Fiorucci, Leaky covariant phase spaces in general relativity, Theory and application to Λ-BMS symmetry, Ph.D. thesis, ULB. 2112.07666
R. Ruzziconi, Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group, lecture notes, PoS Modave 2019, 1910.08367
G. Barnich and F. Del Monte, Introduction to Classical Gauge Field Theory and to Batalin-Vilkovisky Quantization, lecture notes, 22nd Saalburg Summer School (2016), 1810.00442
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press (1994), ISBN: 78-0-691-03769-1, 978-0-691-21386-6
Relevant literature:
G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3-82. hep-th/0111246
J. Lee and R. Wald, Local symmetries and constraints, J. Math. Phys. 31, 725–743 (1990)
G. Barnich and G. Compère, Surface charge algebra in gauge theories and thermodynamic integrability, J. Math. Phys. 49 (2008) 042901, 0708.2378
G. Barnich and C. Troessaert, BMS Charge Algebra, JHEP 12 (2011) 105, 1106.0213
A. Fiorucci and R. Ruzziconi, Charges in Al(A)dSn spacetimes, JHEP 05 (2021) 210, 2011.02002
L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale, Extended corner symmetry, charge bracket and Einstein’s equations, JHEP 09 (2021) 083, 2104.12881
Θα υπάρχει ταυτόχρονη διαδικτυακή μετάδοση μέσω Zoom:
https://authgr.zoom.us/j/96018629921?pwd=hLrSo5za7KV0RJ7uXLXxufuL9Cmk55.1
Meeting ID: 960 1862 9921
Passcode: 990011
