Introduction to Quantum Gravity – Overview

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Outline

The course offers a basic introduction to (part of) current quantum gravity research. First, it introduces the physical and conceptual motivations for constructing such theory, and the main difficulties that can be expected in doing so. Next, the historical paths towards the definition of the theory are surveyed: canonical quantization in ADM variables, path integral quantization of GR, perturbative quantization in the weak field limit. The bulk of the course is an introduction to some of the contemporary quantum gravity formalisms: loop quantum gravity and spin foam models, lattice quantum gravity, tensor models and group field theories. Brief accounts of other quantum gravity formalisms will also be given. Finally, the course includes a survey of various results aiming at identifying quantum gravity effects in physical phenomena, in the context of black holes physics and early universe cosmology, directly from the fundamental formalisms or via more phenomenological strategies.

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Level

Early Master level (basic knowledge of General Relativity and Quantum Field Theory is required, but not more)

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References

1st and 2nd lectures:

J. Butterfield, C. Isham, gr-qc/9903072
C. Isham, gr-qc/9510063
C. Rovelli, hep-th/9910131
S. Carlip, gr-qc/0108040
S. Carlip, arXiv:1507.08194 [gr-qc]
S. Carlip, arXiv:0803.3456 [gr-qc]
A. Ashtekar, M. Reuter, C. Rovelli, arXiv:1408.4336 [gr-qc]
D. Oriti, arXiv:1710.02807 [gr-qc]

3rd - 5th lectures:

D. Giulini, gr-qc/0603087
C. Rovelli, Class.Quant.Grav. 8 (1991) 297-316
C. Rovelli, gr-qc/0110035
C. Isham, gr-qc/9210011
P. Peldan, gr-qc/9305011
K. Kuchar, gr-qc/9304012
C. Kiefer, arXiv:0812.0295 [gr-qc]
C. Kiefer, gr-qc/0611141

6th and 7th lecture:

J. Hartle, K. Kuchar, Phys.Rev. D34 (1986) 2323-2331
J. Halliwell, T. Ortiz, gr-qc/9211004
M. Chaichian, A. Demichev, Path integrals in quantum mechanics, IOP (2001)
A. Zee, QFT in a nutshell, PUP (2003)
R. Rivers, Path integral methods in QFT, CUP (1997)
M. Creutz, Quarks, gluons and lattices, CUP (1983)
R. Oeckl, H. Pfeiffer, hep-th/0008095
P. Peldan, gr-qc/9305011

8th lecture

C. Teitelboim, Phys Rev D25, 3159 (1982)
J. Halliwell, J. Hartle, Phys.Rev. D43 (1991) 1170-1194

9th lecture

H. Hamber, 0704.2895 [hep-th]
J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll, arXiv:1203.3591 [hep-th]

10th lecture

G. ’T Hooft, Erice Lecture, https://www.staff.science.uu.nl/~hooft101/lectures/erice02.pdf
J. Donoghue, 1209.3511 [gr-qc]
R. Woodard, 1407.4748 [gr-qc]

11th lecture

R. Percacci, 0709.3851 [hep-th]
M. Reuter, F. Saueressig, 1202.2274 [hep-th]

12th lecture - loop quantum gravity (programme and kinematics)
13th lecture - loop quantum gravity (dynamics and basic results)

C. Rovelli, Living Rev.Rel. 11 (2008) 5
T. Thiemann, gr-qc/0210094
A. Ashtekar, J. Lewandowski, gr-qc/0404018
K. Giesel, H. Sahlmann, arXiv:1203.2733 [gr-qc]
N. Bodendorfer, arXiv:1607.05129 [gr-qc]

14th and 15th lecture - spin foam models

A. Perez, Living Rev. Relativity 16 (2013) 3, arXiv:1205.2019 [gr-qc]

16th lecture - matrix models

P. Di Francesco, P. Ginsparg, J. Zinn-Justin, arXiv: hep-th/9306153
F. David, arXiv: hep-th/9303127

17th and 18th lecture - tensor models

R. Gurau, J. Ryan, arXiv:1109.4812 [hep-th]
V. Rivasseau, arXiv:1604.07860 [hep-th]

19th - 20th lecture - group field theory

D. Oriti, arXiv: 1110.5606 [hep-th]
T. Krajewski, arXiv: 1210.6257 [gr-qc]
D. Oriti, arXiv: 1408.7112 [hep-th]
S. Carrozza, arXiv: 1603.01902 [gr-qc]
S. Gielen, L. Sindoni, arXiv: 1602.08104 [gr-qc]
D. Oriti, arXiv: 1612.09521 [gr-qc]

21st lecture - Loop quantum cosmology

A. Ashtekar and P. Singh, Class. Quant. Grav. 28 (2011) 213001, arXiv:1108.0893
K. Banerjee, G. Calcagni, M. Mart n-Benito, SIGMA 8 (2012) 016, arXiv:1109.6801
M. Bojowald, Living Rev. Rel. 11 (2008) 4