Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 8 (2012), 010, 26 pages      arXiv:1110.3874      https://doi.org/10.3842/SIGMA.2012.010
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Matter in Loop Quantum Gravity

Ghanashyam Date a and Golam Mortuza Hossain b
a) The Institute of Mathematical Sciences, CIT Campus, Chennai, 600 113, India
b) Department of Physical Sciences, Indian Institute of Science Education and Research - Kolkata, Mohanpur Campus, Nadia - 741 252, WB, India

Received October 16, 2011, in final form February 27, 2012; Published online March 09, 2012

Abstract
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.

Key words: loop quantization; loop quantum gravity; matter in loop quantum gravity.

pdf (542 kb)   tex (45 kb)

References

  1. Alfaro J., Morales-Técotl H.A., Urrutia L.F., Loop quantum gravity and light propagation, Phys. Rev. D 65 (2002), 103509, 18 pages, hep-th/0108061.
  2. Alfaro J., Morales-Técotl H.A., Urrutia L.F., Quantum gravity corrections to neutrino propagation, Phys. Rev. Lett. 84 (2000), 2318-2321, gr-qc/9909079.
  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 pages, hep-th/0208192.
  4. Ashtekar A., Fairhurst S., Willis J.L., Quantum gravity, shadow states and quantum mechanics, Classical Quantum Gravity 20 (2003), 1031-1061, gr-qc/0207106.
  5. Ashtekar A., Kaminski W., Lewandowski J., Quantum field theory on a cosmological, quantum space-time, Phys. Rev. D 79 (2009), 064030, 12 pages, arXiv:0901.0933.
  6. Ashtekar A., Lewandowski J., Background independent quantum gravity: a status report, Classical Quantum Gravity 21 (2004), R53-R152, gr-qc/0404018.
  7. Ashtekar A., Lewandowski J., Sahlmann H., Polymer and Fock representations for a scalar field, Classical Quantum Gravity 20 (2003), L11-L21, gr-qc/0211012.
  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 pages, gr-qc/0604013.
  9. Ashtekar A., Pawlowski T., Singh P., Quantum nature of the big bang: improved dynamics, Phys. Rev. D 74 (2006), 084003, 23 pages, gr-qc/0607039.
  10. Ashtekar A., Rovelli C., Smolin L., Weaving a classical metric with quantum threads, Phys. Rev. Lett. 69 (1992), 237-240, hep-th/9203079.
  11. Ashtekar A., Wilson-Ewing E., Loop quantum cosmology of Bianchi type I models, Phys. Rev. D 79 (2009), 083535, 21 pages, arXiv:0903.3397.
  12. Baez J.C., Krasnov K.V., Quantization of diffeomorphism-invariant theories with fermions, J. Math. Phys. 39 (1998), 1251-1271, hep-th/9703112.
  13. Berezin F.A., The method of second quantization, Pure and Applied Physics, Vol. 24, Academic Press, New York, 1966.
  14. Bojowald M., Das R., Canonical gravity with fermions, Phys. Rev. D 78 (2008), 064009, 16 pages, arXiv:0710.5722.
  15. Bojowald M., Das R., Fermions in loop quantum cosmology and the role of parity, Classical Quantum Gravity 25 (2008), 195006, 23 pages, arXiv:0806.2821.
  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 pages, gr-qc/0411101.
  17. Borissov R., Weave states for plane gravitational waves, Phys. Rev. D 49 (1994), 923-929.
  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 pages, gr-qc/0403053.
  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 pages, arXiv:0811.4496.
  22. DeWitt B., Supermanifolds, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984.
  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, math-ph/0407006.
  25. Freidel L., Minic D., Takeuchi T., Quantum gravity, torsion, parity violation, and all that, Phys. Rev. D 72 (2005), 104002, 6 pages, hep-th/0507253.
  26. Gambini R., Pullin J., Nonstandard optics from quantum space-time, Phys. Rev. D 59 (1999), 124021, 4 pages, gr-qc/9809038.
  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.
  28. Grot N., Rovelli C., Weave states in loop quantum gravity, Gen. Relativity Gravitation 29 (1997), 1039-1048.
  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.
  30. Henneaux M., Teitelboim C., Quantization of gauge systems, Princeton University Press, Princeton, NJ, 1992.
  31. Hollands S., Wald R.M., Axiomatic quantum field theory in curved spacetime, Comm. Math. Phys. 293 (2010), 85-125, arXiv:0803.2003.
  32. Hossain G.M., Husain V., Seahra S.S., Background independent quantization and wave propagation, Phys. Rev. D 80 (2009), 044018, 12 pages, arXiv:0906.4046.
  33. Hossain G.M., Husain V., Seahra S.S., Nonsingular inflationary universe from polymer matter, Phys. Rev. D 81 (2010), 024005, 5 pages, arXiv:0906.2798.
  34. Hossain G.M., Husain V., Seahra S.S., Propagator in polymer quantum field theory, Phys. Rev. D 82 (2010), 124032, 5 pages, arXiv:1007.5500.
  35. Husain V., Kreienbuehl A., Ultraviolet behavior in background independent quantum field theory, Phys. Rev. D 81 (2010), 084043, 7 pages, arXiv:1002.0138.
  36. Iwasaki J., Basis states for gravitons in non-perturbative loop representation space, gr-qc/9807013.
  37. Iwasaki J., Rovelli C., Gravitons as embroidery on the weave, Internat. J. Modern Phys. D 1 (1992), 533-557.
  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.
  39. Jacobson T., Fermions in canonical gravity, Classical Quantum Gravity 5 (1988), L143-L148.
  40. Jain P., Ralston J.P., Supersymmetry and the Lorentz fine tuning problem, Phys. Lett. B 621 (2005), 213-218, hep-ph/0502106.
  41. Kaul R.K., Holst actions for supergravity theories, Phys. Rev. D 77 (2008), 045030, 8 pages, arXiv:0711.4674.
  42. Kaul R.K., Sengupta S., Topological parameters in gravity, Phys. Rev. D 85 (2012), 024026, 15 pages, arXiv:1106.3027.
  43. Laddha A., Varadarajan M., Polymer parametrized field theory, Phys. Rev. D 78 (2008), 044008, 22 pages, arXiv:0805.0208.
  44. Laddha A., Varadarajan M., Polymer quantization of the free scalar field and its classical limit, Classical Quantum Gravity 27 (2010), 175010, 45 pages, arXiv:1001.3505.
  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, gr-qc/0504147.
  46. Mattingly D., Modern tests of Lorentz invariance, Living Rev. Relativity 8 (2005), 5, 84 pages, gr-qc/0502097.
  47. Mercuri S., Fermions in the Ashtekar-Barbero connection formalism for arbitrary values of the Immirzi parameter, Phys. Rev. D 73 (2006), 084016, 14 pages, gr-qc/0601013.
  48. Mercuri S., Nieh-Yan invariant and Fermions in Ashtekar-Barbero-Immirzi formalism, 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, gr-qc/9506073.
  50. Morales-Técotl H.A., Rovelli C., Fermions in quantum gravity, Phys. Rev. Lett. 72 (1994), 3642-3645, gr-qc/9401011.
  51. Morales-Técotl H.A., Rovelli C., Loop space representation of quantum fermions and gravity, Nuclear Phys. B 451 (1995), 325-361.
  52. Nicolai H., Peeters K., Zamaklar M., Loop quantum gravity: an outside view, Classical Quantum Gravity 22 (2005), R193-R247, hep-th/0501114.
  53. Perez A., Rovelli C., Physical effects of the Immirzi parameter in loop quantum gravity, Phys. Rev. D 73 (2006), 044013, 3 pages, gr-qc/0505081.
  54. Rezende D.J., Perez A., Four-dimensional Lorentzian Holst action with topological terms, Phys. Rev. D 79 (2009), 064026, 11 pages, arXiv:0902.3416.
  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, gr-qc/0207030.
  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, gr-qc/0207031.
  57. Sengupta S., Kaul R.K., Canonical supergravity with Barbero-Immirzi parameter, Phys. Rev. D 81 (2010), 024024, 7 pages, arXiv:0909.4850.
  58. Thiemann T., Kinematical Hilbert spaces for fermionic and Higgs quantum field theories, Classical Quantum Gravity 15 (1998), 1487-1512, gr-qc/9705021.
  59. Thiemann T., Quantum spin dynamics (QSD), Classical Quantum Gravity 15 (1998), 839-873, gr-qc/9606089.
  60. Thiemann T., Quantum spin dynamics (QSD). II. The kernel of the Wheeler-DeWitt constraint operator, Classical Quantum Gravity 15 (1998), 875-905, gr-qc/9606090.
  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, gr-qc/9705019.
  62. Varadarajan M., Photons from quantized electric flux representations, Phys. Rev. D 64 (2001), 104003, 9 pages, gr-qc/0104051.
  63. Wald R.M., Quantum field theory on curved space-times and black hole thermodynamics, The University of Chicago Press, Chicago, 1994.
  64. Weyl H., A remark on the coupling of gravitation and electron, Phys. Rev. 77 (1950), 699-701.
  65. Zegwaard J., The weaving of curved geometries, Phys. Lett. B 300 (1993), 217-222, hep-th/9210033.

Previous article  Next article   Contents of Volume 8 (2012)