Matter in loop quantum gravity
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also requires a non-standard quantum representation of matter. While loop quantization of standard model fields has been proposed, detail study of its implications is not yet available. This review aims to survey the various efforts and results.
Keywords: loop quantum gravity, matter in loop quantum gravity.
Mots-clés : loop quantization
@article{SIGMA_2012_8_a9,
     author = {Ghanashyam Date and Golam Mortuza Hossain},
     title = {Matter in loop quantum gravity},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a9/}
}
TY  - JOUR
AU  - Ghanashyam Date
AU  - Golam Mortuza Hossain
TI  - Matter in loop quantum gravity
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2012
VL  - 8
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a9/
LA  - en
ID  - SIGMA_2012_8_a9
ER  - 
%0 Journal Article
%A Ghanashyam Date
%A Golam Mortuza Hossain
%T Matter in loop quantum gravity
%J Symmetry, integrability and geometry: methods and applications
%D 2012
%V 8
%U http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a9/
%G en
%F SIGMA_2012_8_a9
Ghanashyam Date; Golam Mortuza Hossain. Matter in loop quantum gravity. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a9/

[1] Alfaro J., Morales-Técotl H.A., Urrutia L.F., “Loop quantum gravity and light propagation”, Phys. Rev. D, 65 (2002), 103509, 18 pp. ; arXiv: hep-th/0108061 | DOI | MR

[2] Alfaro J., Morales-Técotl H.A., Urrutia L.F., “Quantum gravity corrections to neutrino propagation”, Phys. Rev. Lett., 84 (2000), 2318–2321 ; arXiv: gr-qc/9909079 | DOI

[3] Alfaro J., Morales-Técotl H.A., Urrutia L.F., “Quantum gravity and spin-1/2 particle effective dynamics”, Phys. Rev. D, 66 (2002), 124006, 19 pp. ; arXiv: hep-th/0208192 | DOI | MR | Zbl

[4] Ashtekar A., Fairhurst S., Willis J.L., “Quantum gravity, shadow states and quantum mechanics”, Classical Quantum Gravity, 20 (2003), 1031–1061 ; arXiv: gr-qc/0207106 | DOI | MR | Zbl

[5] Ashtekar A., Kaminski W., Lewandowski J., “Quantum field theory on a cosmological, quantum space-time”, Phys. Rev. D, 79 (2009), 064030, 12 pp. ; arXiv: 0901.0933 | DOI | MR

[6] Ashtekar A., Lewandowski J., “Background independent quantum gravity: a status report”, Classical Quantum Gravity, 21 (2004), R53–R152 ; arXiv: gr-qc/0404018 | DOI | MR | Zbl

[7] Ashtekar A., Lewandowski J., Sahlmann H., “Polymer and Fock representations for a scalar field”, Classical Quantum Gravity, 20 (2003), L11–L21 ; arXiv: gr-qc/0211012 | DOI | MR | Zbl

[8] Ashtekar A., Pawlowski T., Singh P., “Quantum nature of the big bang: an analytical and numerical investigation”, Phys. Rev. D, 73 (2006), 124038, 33 pp. ; arXiv: gr-qc/0604013 | DOI | MR

[9] Ashtekar A., Pawlowski T., Singh P., “Quantum nature of the big bang: improved dynamics”, Phys. Rev. D, 74 (2006), 084003, 23 pp. ; arXiv: gr-qc/0607039 | DOI | MR | Zbl

[10] Ashtekar A., Rovelli C., Smolin L., “Weaving a classical metric with quantum threads”, Phys. Rev. Lett., 69 (1992), 237–240 ; arXiv: hep-th/9203079 | DOI | MR | Zbl

[11] Ashtekar A., Wilson-Ewing E., “Loop quantum cosmology of Bianchi type I models”, Phys. Rev. D, 79 (2009), 083535, 21 pp. ; arXiv: 0903.3397 | DOI | MR

[12] Baez J.C., Krasnov K.V., “Quantization of diffeomorphism-invariant theories with fermions”, J. Math. Phys., 39 (1998), 1251–1271 ; arXiv: hep-th/9703112 | DOI | MR | Zbl

[13] Berezin F.A., The method of second quantization, Pure and Applied Physics, 24, Academic Press, New York, 1966 | MR | Zbl

[14] Bojowald M., Das R., “Canonical gravity with fermions”, Phys. Rev. D, 78 (2008), 064009, 16 pp. ; arXiv: 0710.5722 | DOI | MR

[15] Bojowald M., Das R., “Fermions in loop quantum cosmology and the role of parity”, Classical Quantum Gravity, 25 (2008), 195006, 23 pp. ; arXiv: 0806.2821 | DOI | MR | Zbl

[16] Bojowald M., Morales-Técotl H.A., Sahlmann H., “Loop quantum gravity phenomenology and the issue of Lorentz invariance”, Phys. Rev. D, 71 (2005), 084012, 7 pp. ; arXiv: gr-qc/0411101 | DOI | MR

[17] Borissov R., “Weave states for plane gravitational waves”, Phys. Rev. D, 49 (1994), 923–929 | DOI | MR

[18] Collins J., Perez A., Sudarsky D., Urrutia L., Vucetich H., “Lorentz invariance and quantum gravity: an additional fine-tuning problem?”, Phys. Rev. Lett., 93 (2004), 191301, 4 pp. ; arXiv: gr-qc/0403053 | DOI | MR

[19] Date G., Lectures on LQG/LQC, arXiv: 1004.2952

[20] Date G., Revisiting canonical gravity with fermion, arXiv: 1110.3416

[21] Date G., Kaul R.K., Sengupta S., “Topological interpretation of Barbero–Immirzi parameter”, Phys. Rev. D, 79 (2009), 044008, 7 pp. ; arXiv: 0811.4496 | DOI | MR

[22] DeWitt B., Supermanifolds, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984 | MR | Zbl

[23] Fell J.M.G., Doran R.S., Representations of $*$-algebras, locally compact groups, and Banach $*$-algebraic bundles, Academic Press, Boston, 1988

[24] Fleischhack C., “Representations of the Weyl algebra in quantum geometry”, Comm. Math. Phys., 285 (2009), 67–140 ; arXiv: math-ph/0407006 | DOI | MR

[25] Freidel L., Minic D., Takeuchi T., “Quantum gravity, torsion, parity violation, and all that”, Phys. Rev. D, 72 (2005), 104002, 6 pp. ; arXiv: hep-th/0507253 | DOI | MR

[26] Gambini R., Pullin J., “Nonstandard optics from quantum space-time”, Phys. Rev. D, 59 (1999), 124021, 4 pp. ; arXiv: gr-qc/9809038 | DOI | MR

[27] Gambini R., Pullin J., Rastgoo S., “Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case”, Gen. Relativity Gravitation, 43 (2011), 3569–3592 ; arXiv: 1105.0667 | DOI | Zbl

[28] Grot N., Rovelli C., “Weave states in loop quantum gravity”, Gen. Relativity Gravitation, 29 (1997), 1039–1048 | DOI | MR | Zbl

[29] Hehl F.W., von der Heyde P., Kerlick G.D., Nester J.M., “General relativity with spin and torsion: foundations and prospect”, Rev. Modern Phys., 48 (1976), 393–416 | DOI | MR

[30] Henneaux M., Teitelboim C., Quantization of gauge systems, Princeton University Press, Princeton, NJ, 1992 | MR | Zbl

[31] Hollands S., Wald R.M., “Axiomatic quantum field theory in curved spacetime”, Comm. Math. Phys., 293 (2010), 85–125 ; arXiv: 0803.2003 | DOI | MR | Zbl

[32] Hossain G.M., Husain V., Seahra S.S., “Background independent quantization and wave propagation”, Phys. Rev. D, 80 (2009), 044018, 12 pp. ; arXiv: 0906.4046 | DOI | MR

[33] Hossain G.M., Husain V., Seahra S.S., “Nonsingular inflationary universe from polymer matter”, Phys. Rev. D, 81 (2010), 024005, 5 pp. ; arXiv: 0906.2798 | DOI

[34] Hossain G.M., Husain V., Seahra S.S., “Propagator in polymer quantum field theory”, Phys. Rev. D, 82 (2010), 124032, 5 pp. ; arXiv: 1007.5500 | DOI

[35] Husain V., Kreienbuehl A., “Ultraviolet behavior in background independent quantum field theory”, Phys. Rev. D, 81 (2010), 084043, 7 pp. ; arXiv: 1002.0138 | DOI

[36] Iwasaki J., Basis states for gravitons in non-perturbative loop representation space, arXiv: gr-qc/9807013

[37] Iwasaki J., Rovelli C., “Gravitons as embroidery on the weave”, Internat. J. Modern Phys. D, 1 (1992), 533–557 | DOI | MR | Zbl

[38] Iwasaki J., Rovelli C., “Gravitons from loops: non-perturbative loop-space quantum gravity contains the graviton-physics approximation”, Classical Quantum Gravity, 11 (1994), 1653–1676 | DOI | MR

[39] Jacobson T., “Fermions in canonical gravity”, Classical Quantum Gravity, 5 (1988), L143–L148 http://stacks.iop.org/0264-9381/5/L143 | DOI | MR

[40] Jain P., Ralston J.P., “Supersymmetry and the {L}orentz fine tuning problem”, Phys. Lett. B, 621 (2005), 213–218 ; arXiv: hep-ph/0502106 | DOI | MR

[41] Kaul R.K., “Holst actions for supergravity theories”, Phys. Rev. D, 77 (2008), 045030, 8 pp. ; arXiv: 0711.4674 | DOI | MR

[42] Kaul R.K., Sengupta S., “Topological parameters in gravity”, Phys. Rev. D, 85 (2012), 024026, 15 pp. ; arXiv: 1106.3027 | DOI | MR

[43] Laddha A., Varadarajan M., “Polymer parametrized field theory”, Phys. Rev. D, 78 (2008), 044008, 22 pp. ; arXiv: 0805.0208 | DOI

[44] Laddha A., Varadarajan M., “Polymer quantization of the free scalar field and its classical limit”, Classical Quantum Gravity, 27 (2010), 175010, 45 pp. ; arXiv: 1001.3505 | DOI | MR | Zbl

[45] Lewandowski J., Okolów A., Sahlmann H., Thiemann T., “Uniqueness of diffeomorphism invariant states on holonomy-flux algebras”, Comm. Math. Phys., 267 (2006), 703–733 ; arXiv: gr-qc/0504147 | DOI | MR | Zbl

[46] Mattingly D., “Modern tests of Lorentz invariance”, Living Rev. Relativity, 8 (2005), 5, 84 pp. ; arXiv: gr-qc/0502097 | Zbl

[47] Mercuri S., “Fermions in the Ashtekar–{B}arbero connection formalism for arbitrary values of the Immirzi parameter”, Phys. Rev. D, 73 (2006), 084016, 14 pp. ; arXiv: gr-qc/0601013 | DOI | MR

[48] Mercuri S., Nieh–Yan invariant and Fermions in Ashtekar–Barbero–Immirzi formalism, arXiv: gr-qc/0610026

[49] Morales-Técotl H.A., Esposito G., “Self-dual action for fermionic fields and gravitation”, Nuovo Cimento B, 109 (1994), 973–982 ; arXiv: gr-qc/9506073 | DOI | MR

[50] Morales-Técotl H.A., Rovelli C., “Fermions in quantum gravity”, Phys. Rev. Lett., 72 (1994), 3642–3645 ; arXiv: gr-qc/9401011 | DOI | MR | Zbl

[51] Morales-Técotl H.A., Rovelli C., “Loop space representation of quantum fermions and gravity”, Nuclear Phys. B, 451 (1995), 325–361 | DOI | MR | Zbl

[52] Nicolai H., Peeters K., Zamaklar M., “Loop quantum gravity: an outside view”, Classical Quantum Gravity, 22 (2005), R193–R247 ; arXiv: hep-th/0501114 | DOI | MR | Zbl

[53] Perez A., Rovelli C., “Physical effects of the Immirzi parameter in loop quantum gravity”, Phys. Rev. D, 73 (2006), 044013, 3 pp. ; arXiv: gr-qc/0505081 | DOI | MR

[54] Rezende D.J., Perez A., “Four-dimensional Lorentzian Holst action with topological terms”, Phys. Rev. D, 79 (2009), 064026, 11 pp. ; arXiv: 0902.3416 | DOI | MR

[55] Sahlmann H., Thiemann T., “Towards the {QFT} on curved spacetime limit of QGR. I. A general scheme”, Classical Quantum Gravity, 23 (2006), 867–908 ; arXiv: gr-qc/0207030 | DOI | MR | Zbl

[56] Sahlmann H., Thiemann T., “Towards the QFT on curved spacetime limit of QGR. II. A concrete implementation”, Classical Quantum Gravity, 23 (2006), 909–954 ; arXiv: gr-qc/0207031 | DOI | MR | Zbl

[57] Sengupta S., Kaul R.K., “Canonical supergravity with Barbero–Immirzi parameter”, Phys. Rev. D, 81 (2010), 024024, 7 pp. ; arXiv: 0909.4850 | DOI | MR

[58] Thiemann T., “Kinematical Hilbert spaces for fermionic and Higgs quantum field theories”, Classical Quantum Gravity, 15 (1998), 1487–1512 ; arXiv: gr-qc/9705021 | DOI | MR | Zbl

[59] Thiemann T., “Quantum spin dynamics (QSD)”, Classical Quantum Gravity, 15 (1998), 839–873 ; arXiv: gr-qc/9606089 | DOI | MR | Zbl

[60] Thiemann T., “Quantum spin dynamics (QSD). II. The kernel of the Wheeler–DeWitt constraint operator”, Classical Quantum Gravity, 15 (1998), 875–905 ; arXiv: gr-qc/9606090 | DOI | MR | Zbl

[61] Thiemann T., “Quantum spin dynamics (QSD). V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories”, Classical Quantum Gravity, 15 (1998), 1281–1314 ; arXiv: gr-qc/9705019 | DOI | MR | Zbl

[62] Varadarajan M., “Photons from quantized electric flux representations”, Phys. Rev. D, 64 (2001), 104003, 9 pp. ; arXiv: gr-qc/0104051 | DOI | MR

[63] Wald R.M., Quantum field theory on curved space-times and black hole thermodynamics, The University of Chicago Press, Chicago, 1994 | MR

[64] Weyl H., “A remark on the coupling of gravitation and electron”, Phys. Rev., 77 (1950), 699–701 | DOI | MR

[65] Zegwaard J., “The weaving of curved geometries”, Phys. Lett. B, 300 (1993), 217–222 ; arXiv: hep-th/9210033 | DOI | MR