The microscopic dynamics of quantum space as a group field theory

doi:10.1017/CBO9780511920998.012

12 - The microscopic dynamics of quantum space as a group field theory

Published online by Cambridge University Press: 05 August 2012

Edited by

Amanda Weltman and

Daniele Oriti: Affiliation:
Max-Planck-Institut für Gravitationsphysik
Jeff Murugan: Affiliation:
University of Cape Town
Amanda Weltman: Affiliation:
University of Cape Town
George F. R. Ellis: Affiliation:
University of Cape Town

Book contents

Get access

Summary

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3D Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on some recent results, concerning both the mathematical definition of GFT models as bona fide field theories, and avenues towards extracting testable physics from them.

Introduction

The field of non-perturbative and background-independent quantum gravity has progressed considerably over the past few decades [78]. New research directions are being developed, new important developments are taking place in existing approaches, and some of these approaches are converging to one another. As a result, ideas and tools from one become relevant to another, and trigger further progress. The group field theory (GFT) formalism [39, 77, 79] nicely captures this convergence of approaches and ideas. It is a generalization of the much studied matrix models for 2D quantum gravity and string theory [28, 53]. At the same time, it generalizes it, as we are going to explain, by incorporating the insights coming from canonical loop quantum gravity and its covariant spin foam formulation of the dynamics, and so it became an important part of this approach to the quantization of 4D gravity [72, 74, 81, 85]. Furthermore, it is a point of convergence of the same loop quantum gravity approach and of simplicial quantum gravity approaches, like quantum Regge calculus [93] and dynamical triangulations [3, 79], in that the covariant dynamics of the first takes the form, as we are going to see, of simplicial path integrals.

Information

Type: Chapter
Information: Foundations of Space and Time
Reflections on Quantum Gravity
, pp. 257 - 320

DOI: https://doi.org/10.1017/CBO9780511920998.012 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

[1] S., Alexandrov, Phys. Rev.D 78, 044033 (2008) [arXiv: 0802.3389 [gr-qc]].

[2] J., Ambjørn, B., Durhuus, T., Jonsson, Mod. Phys. Lett. A6, 1133–46 (1991).

[3] J., Ambjørn, J., Jurkiewicz, R., Loll, Phys. Rev.D 72, 064014 (2005) [arXiv: hep-th/0505154].

[4] G., Amelino-Camelia, Lect. Notes Phys. 669, 59–100 (2004) [arXiv: gr-qc/0412136].

[5] P., Anspinwall, B., Greene, D., Morrison, Nucl. Phys.B 416, 414–80 (1994) hep-th/9309097.

[6] J. C., Baez, J. W., Barrett, Adv. Theor. Math. Phys. 3, 815 (1999) gr-qc/9903060.

[7] T., Banks, Nucl. Phys. B 309, 493 (1988).

[8] A., Baratin, C., Flori, T., Thiemann [arXiv: 0812.4055 [gr-qc]].

[9] A., Baratin, B., Dittrich, D., Oriti, J., Tambornino (2010), [arXiv:1004.3450 [hep-th]].

[10] A., Baratin, F., Girelli, D., Oriti (2010), [arXiv:1101.0590 [hep-th]].

[11] A., Baratin, D., Oriti [arXiv: 1002.4723 [hep-th]].

[12] A., Baratin, D., Oriti (2010), to appear.

[13] A., Baratin, D., Oriti (2010), Phys. Rev. Lett. 105 221302 (2010).

[14] A., Barbieri, Nucl. Phys.B 518, 714 (1998) gr-qc/9707010.

[15] C., Barcelo, S., Liberati, M., Visser, Living Rev. Rel. 8, 12 (2005) [arXiv: gr-qc/0505065].

[16] J. W., Barrett, L., Crane, J. Math. Phys. 39, 3296 (1998), gr-qc/9709028.

[17] J., Barrett, R., Dowdall, W., Fairbairn, H., Gomes, F., Hellman, J. Math. Phys. 50, 112504 (2009), [arXiv:0902.1170 [gr-qc]].

[18] J., Barrett, R., Dowdall, W., Fairbairn, F., Hellman, R., Pereira, Class. Quant. Grav. 27, 165009 (2010) [arXiv: 0907.2440 [gr-qc]].

[19] J., Barrett, I., Naish-Guzman, Class. Quant. Grav. 26, 155014 (2009) [arXiv: 0803.3319 [gr-qc]].

[20] J., Ben Geloun, J., Magnen, V., RivasseauEuro. Phys. J. C70, 1119–30 (2010) [arXiv: 0911.1719 [hep-th]].

[21] J., Ben Geloun, T., Krajewski, J., Magnen, V., RivasseauClass. Quant. Grav. 27, 155012 (2010) [arXiv: 1002.3592 [hep-th]].

[22] M., Bojowald, Living Rev. Rel. 11, 4 (2008).

[23] V., Bonzom, E., LivinePhys. Rev. D79, 064034 (2009) [arXiv:0812.3456].

[24] D., V. Boulatov, Mod. Phys. Lett. A7, 1629–46 (1992) [arXiv:hep-th/9202074].

[25] S., Coleman, Nucl. Phys.B 310, 643 (1988).

[26] F., Conrady, L., Freidel, Phys. Rev.D 78, 104023 (2008) [arXiv: 0809.2280].

[27] F., Conrady, L., Freidel, Class. Quant. Grav. 25, 245010 (2008) [arXiv: 0806.4640].

[28] F., David, Nucl. Phys.B 257, 45 (1985).

[29] R., De Pietri, L., Freidel, Class. Quant. Grav. 16, 2187 (1999) gr-qc/9804071.

[30] R., De Pietri, L., Freidel, K., Krasnov, C., Rovelli, Nucl. Phys.B 574, 785 (2000) [arXiv: hep-th/9907154].

[31] B., Dittrich, [arXiv:0810.3594[gr-qc]].

[32] B., Dittrich, J., RyanPhys. Rev. D82, 064026 (2010) [arXiv:0807.2806].

[33] F., Dowker, R., Sorkin, Class. Quant. Grav. 15, 1153–67 (1998) gr-qc/9609064.

[34] F., Dowker, in The Future of Theoretical Physics and Cosmology, 436–52, Cambridge University Press (2002), gr-qc/0206020.

[35] J., Engle, R., Pereira, C., Rovelli, Phys. Rev. Lett. 99, 161301 (2007) [arXiv: 0705.2388].

[36] J., Engle, R., Pereira, C., Rovelli, Nucl. Phys.B 798, 251 (2008) [arXiv: 0708.1236].

[37] J., Engle, E., Livine, R., Pereira, C., Rovelli, Nucl. Phys.B 799, 136 (2008) [arXiv:0711.0146].

[38] W., Fairbairn, E., Livine, Class. Quant. Grav. 24, 5277 (2007) [arXiv: gr-qc/0702125].

[39] L., Freidel, Int. J. Phys. 44, 1769–83, (2005) [arXiv: hep-th/0505016].

[40] L., Freidel, R., Gurau, D., Oriti, Phys. Rev.D 80, 044007 (2009) [arXiv: 0905.3772].

[41] L., Freidel, J., Kowalski-Glikman, S., Nowak (2007), arXiv:0706.3658 [hep-th].

[42] L., Freidel, K., Krasnov, Class. Quant. Grav. 25, 125018 (2008) [arXiv: 0708.1595].

[43] L., Freidel, E., Livine, Class. Quant. Grav. 23, 2021 (2006) [arXiv: hep-th/0502106].

[44] L., Freidel, E., Livine, C., Rovelli, Class. Quant. Grav. 20, 1463–78 (2003) [arXiv: gr-qc/0212077].

[45] L., Freidel, D., Louapre, Phys. Rev.D 68, 104004 (2003) [arXiv: hep-th/0211026].

[46] L., Freidel, D., Louapre, Nucl. Phys.B 662, 279–98, 2003 [arXiv: gr-qc/0212001].

[47] L., Freidel, D., Louapre, Class. Quant. Grav. 21, 5685–726 (2004) [arXiv: hep-th/0401076].

[48] L., Freidel, D., Louapre [arXiv: gr-qc/0410141].

[49] L., Freidel, S., Majid, Class. Quant. Grav. 25, 045006 (2008) [arXiv:hep-th/0601004].

[50] L., Freidel, A., Starodubtsev (2005) arXiv:hep-th/0501191.

[51] M., Gaul, C., Rovelli, Lect. Notes Phys. 541, 277 (2000) gr-qc/9910079.

[52] S., Giddings, A., Strominger, Nucl. Phys.B 321, 481 (1989).

[53] P., Ginsparg, “Matrix models of 2-d gravity”, [arXiv: hep-th/9112013].

[54] F., Girelli, E., Livine, D., Oriti, Phys. Rev.D 81, 024015 (2010) [arXiv: 0903.3475 [gr-qc]].

[55] D., Giulini, Gen. Rel. Grav. 41, 785–815 (2009) [arXiv:0902.3923].

[56] M., Gross, Nucl. Phys. Proc. Suppl. 25A, 144–149 (1992).

[57] R., Gurau [arXiv:0907.2582 [hep-th]].

[58] R., Gurau [arXiv:0911.1945 [hep-th]].

[59] G., Horowitz, Class. Quant. Grav. 8, 587–602 (1991).

[60] B. L., Hu, Int. J. Theor. Phys. 44 (2005) 1785–806 [arXiv:gr-qc/0503067].

[61] C., Isham, gr-qc/9510063.

[62] E., Joung, J., Mourad, K., Noui, J. Math. Phys. 50, 052503 (2009) [arXiv:0806.4121 [hep-th]].

[63] A., Klimyk, N., Vilenkin, Representations of Lie Groups and Special Functions, Springer Ed. (1995).

[64] J., Kowalski-Glikman, A., Starodubtsev, Phys. Rev.D 78, 084039 (2008), arXiv:0808.2613.

[65] K., Kuchar, in Winnipeg 1991, Proceedings, General Relativity and Relativistic Astrophysics, pp. 211–314.

[66] E., LivineClass. Quant. Grav. 26, 195014 (2009) [arXiv:0811.1462 [gr-qc]].

[67] E., Livine, S., Speziale, Europhys. Lett. 81, 50004 (2008) [arXiv:0708.1915 [gr-qc]].

[68] J., Magnen, K., Noui, V., Rivasseau, M., Smerlak, Class. Quant. Grav. 26, 185012 (2009) [arXiv:0906.5477].

[69] S., Majid, Foundations of Quantum Group Theory, Cambridge University Press (1995).

[70] M., McGuigan, Phys. Rev.D 38, 3031 (1988).

[71] H., Ooguri, Mod. Phys. Lett. A7, 2799 (1992) hep-th/9205090.

[72] D., Oriti, Rept. Prog. Phys. 64, 1489 (2001) [arXiv: gr-qc/0106091].

[73] D., Oriti, Phys. Lett.B 532, 363–72 (2002) [arXiv: gr-qc/0201077].

[74] D., Oriti, PhD thesis, University of Cambridge (2003) [arXiv: gr-qc/0311066].

[75] D., Oriti, in Quantum Gravity, B., Fauser, J., Tolksdorf, E., Zeidler (eds.), Birkhaeuser, Basel (2007) [arXiv: gr-qc/0512103].

[76] D., Oriti [arXiv:gr-qc/0607032].

[77] D., Oriti, Proceedings of Science [arXiv:0710.3276].

[78] D., Oriti (ed.), Approaches to Quantum Gravity, Cambridge University Press, Cambridge (2009).

[79] D., Oriti, J., Ryan, Class. Quant. Grav. 23, 6543 (2006) [arXiv: gr-qc/0602010].

[80] A., Perelomov, Generalized Coherent States and their Applications, Springer, Berlin (1986).

[81] A., Perez, Class. Quant. Grav. 20, R43 (2003) [arXiv: gr-qc/0301113].

[82] A., Perez, C., Rovelli, Nucl. Phys.B 599, 255 (2001) [arXiv: gr-qc/0006107].

[83] M. P., Reisenberger, gr-qc/9804061.

[84] C., Rovelli, in the Proceedings of the 9th Marcel Grossmann Meeting, Rome, Italy (2000), V. G., Gurzadyan et al. (eds), Singapore, World Scientific, gr-qc/0006061.

[85] C., Rovelli, Quantum Gravity, Cambridge University Press, Cambridge (2006).

[86] L., Smolin, in D., Rickles (ed.), The Structural Foundations of Quantum Gravity, pp. 196–239, hep-th/0507235.

[87] R., Sorkin, Int. J. Theor. Phys. 30, 923–48 (1991).

[88] R., Sorkin, Int. J. Theor. Phys. 36, 2759–81 (1997) gr-qc/9706002.

[89] C., Teitelboim, Phys. Rev.D 25, 3159 (1982).

[90] T., Thiemann, Modern Canonical Quantum general Relativity, Cambridge University Press, Cambridge (2007).

[91] V., Turaev, O., Viro, Topology 31, 865 (1992).

[92] G. E., Volovik, Proceedings of MG11, session “Analog Models of and for General Relativity”, arXiv:gr-qc/0612134.

[93] R., Williams, in [78].

Accessibility standard: Unknown

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.