Built on

R. Loll, “Quantum Gravity from Causal Dynamical Triangulations: A Review,” Class. Quant. Grav
Original
1905
Earlier work this paper cites.
L. Freidel, E. R. Livine, and D. Pranzetti, “Gravitational edge modes: from Kac–Moody charges to Poincaré networks,” Class. Quant. Grav
Original
1906
Earlier work this paper cites.
M. Geiller and P. Jai-akson, “Extended actions, dynamics of edge modes, and entanglement entropy,” JHEP
Original
1912
Earlier work this paper cites.
J. v. Neumann, “Uber einen satz von herrn m. h. stone,” Annals of Mathematics
1932
Earlier work this paper cites.
M. H. Stone, “On one-parameter unitary groups in hilbert space,” Annals of Mathematics
1932
Earlier work this paper cites.
E. P. Wigner, “On Unitary Representations of the Inhomogeneous Lorentz Group,” Annals Math
1939
Earlier work this paper cites.
E. P. Wigner, “Relativistische wellengleichungen,” Zeitschrift für Physik
1948
Earlier work this paper cites.
E. P. Wigner and V. Bargmann, “Group theoretical discussion of relativistic wave equations,” Proceedings of the National Academy of Sciences of the United States of America
1948
Earlier work this paper cites.
G. W. Mackey, “On induced representations of groups.,” American Journal of Mathematics
1951
Earlier work this paper cites.
G. W. Mackey, “Induced representations of locally compact groups i,” Annals of Mathematics
1952
Earlier work this paper cites.
G. W. Mackey, “Induced representations of locally compact groups ii,” Annals of Mathematics
1953
Earlier work this paper cites.
V. Bargmann, “On unitary ray representations of continuous groups,” Annals of Mathematics
1954
Earlier work this paper cites.
G. W. Mackey, “Unitary representations of group extensions. i.,” Acta Math
1958
Earlier work this paper cites.
A. A. Kirillov, “Unitary representations of nilpotent lie groups,” Russian Mathematical Surveys
1962
Earlier work this paper cites.
Springer Berlin, Heidelberg, 1976
A. A. Kirillov, Elements of the Theory of Representations · 1976
Earlier work this paper cites.

Similar

Springer Berlin Heidelberg, Berlin, Heidelberg, 1990
A. A. Kirillov, Geometric Quantization · 1990
Cited alongside, same era.
J. Ambjorn and R. Loll, “Nonperturbative Lorentzian quantum gravity, causality and topology change,” Nucl. Phys. B
1998
Cited alongside, same era.
A. A. Kirillov, “Merits and demerits of the orbit method,” Bull. Amer. Math. Soc
1999
Cited alongside, same era.
American Mathematical Society, 2004
A. A. Kirillov, Lectures on the Orbit Method · 2004
Cited alongside, same era.
L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part I. Corner potentials and charges,” JHEP
Original
2006
Cited alongside, same era.
L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part II. Corner metric and Lorentz charges,” JHEP

Then

M. Geiller, “Lorentz-diffeomorphism edge modes in 3d gravity,” JHEP
Original
2018
Later among the works it cites.
G. Wong, “A note on entanglement edge modes in Chern Simons theory,” JHEP
Original
2018
Later among the works it cites.
L. Ciambelli and R. G. Leigh, “Isolated surfaces and symmetries of gravity,” Phys. Rev. D
Original
2021
Later among the works it cites.
D. Anninos and E. Harris, “Three-dimensional de Sitter horizon thermodynamics,” JHEP
Original
2021
Later among the works it cites.
M. Arzano, “Vacuum thermal effects in flat space-time from conformal quantum mechanics,” JHEP
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2024

Quantum Corner Symmetry: Representations and Gluing

Ciambelli, Luca, Kowalski-Glikman, Jerzy, Varrin, Ludovic

Understand

The corner symmetry algebra organises the physical charges induced by gravity on codimension-$2$ corners of a manifold.

In this letter, we initiate a study of the quantum properties of this group using as a toy model the corner symmetry group of two-dimensional gravity $\mathrm{SL}\left(2,\mathbb{R}\right)\ltimes \mathbb{R}^2$.
We first describe the central extensions and how the quantum corner symmetry group arises and give the Casimirs.
We then make use of one particular representation to discuss the gluing of corners, achieved by identifying the maximal commuting sub-algebra.

Built on

R. Loll, “Quantum Gravity from Causal Dynamical Triangulations: A Review,” Class. Quant. Grav
Original
1905
Earlier work this paper cites.
L. Freidel, E. R. Livine, and D. Pranzetti, “Gravitational edge modes: from Kac–Moody charges to Poincaré networks,” Class. Quant. Grav
Original
1906
Earlier work this paper cites.
M. Geiller and P. Jai-akson, “Extended actions, dynamics of edge modes, and entanglement entropy,” JHEP
Original
1912
Earlier work this paper cites.
J. v. Neumann, “Uber einen satz von herrn m. h. stone,” Annals of Mathematics
1932
Earlier work this paper cites.
M. H. Stone, “On one-parameter unitary groups in hilbert space,” Annals of Mathematics
1932
Earlier work this paper cites.
E. P. Wigner, “On Unitary Representations of the Inhomogeneous Lorentz Group,” Annals Math
1939
Earlier work this paper cites.
E. P. Wigner, “Relativistische wellengleichungen,” Zeitschrift für Physik
1948
Earlier work this paper cites.
E. P. Wigner and V. Bargmann, “Group theoretical discussion of relativistic wave equations,” Proceedings of the National Academy of Sciences of the United States of America
1948
Earlier work this paper cites.
G. W. Mackey, “On induced representations of groups.,” American Journal of Mathematics
1951
Earlier work this paper cites.
G. W. Mackey, “Induced representations of locally compact groups i,” Annals of Mathematics
1952
Earlier work this paper cites.
G. W. Mackey, “Induced representations of locally compact groups ii,” Annals of Mathematics
1953
Earlier work this paper cites.
V. Bargmann, “On unitary ray representations of continuous groups,” Annals of Mathematics
1954
Earlier work this paper cites.
G. W. Mackey, “Unitary representations of group extensions. i.,” Acta Math
1958
Earlier work this paper cites.
A. A. Kirillov, “Unitary representations of nilpotent lie groups,” Russian Mathematical Surveys
1962
Earlier work this paper cites.
Springer Berlin, Heidelberg, 1976
A. A. Kirillov, Elements of the Theory of Representations · 1976
Earlier work this paper cites.

Similar

Springer Berlin Heidelberg, Berlin, Heidelberg, 1990
A. A. Kirillov, Geometric Quantization · 1990
Cited alongside, same era.
J. Ambjorn and R. Loll, “Nonperturbative Lorentzian quantum gravity, causality and topology change,” Nucl. Phys. B
1998
Cited alongside, same era.
A. A. Kirillov, “Merits and demerits of the orbit method,” Bull. Amer. Math. Soc
1999
Cited alongside, same era.
American Mathematical Society, 2004
A. A. Kirillov, Lectures on the Orbit Method · 2004
Cited alongside, same era.
L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part I. Corner potentials and charges,” JHEP
Original
2006
Cited alongside, same era.
L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part II. Corner metric and Lorentz charges,” JHEP