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Quantum General Relativity


Affiliations
1 Institute for Gravitation and the Cosmos and Physics Department, Penn State, University Park, PA 16802, United States
 

After a brief historical introduction on quantum gravity as a whole, the current status of loop quantum gravity is discussed. Because of space limitation, I could only illustrate recent advances through one example - cosmology of the every early universe - and provide references for results in other main areas.

Keywords

General Relativity, Loop Quantum Gravity, Quantum Gravity.
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  • Einstein, A., Preussische Akad. Wiss., Sitzungsberichte (Berlin), 1916, 688; Meaning of Relativity, Princeton University Press, Princeton, 1945.
  • Rosenfeld, L., Ann. Phys., 1930, 5, 113; Z. Phys., 1930, 65, 587
  • Bronstein, M. P., Phys. Z. Sowjetunion, 1936, 9, 140–157; Deser, S. and Starobinski, A., Gen. Rel. Grav., 2012, 44, 263–265.
  • Bronstein, M. P., Zh. ETF (JETP), 1936, 6, 195; D. J. CirlioLombardo, arXiv:1405.2334.
  • Feynman, R. P., Acta Phys. Pol., 1964, 24, 697–722.
  • DeWitt, B. S., In Magic without Magic: John Archibald Wheeler (ed. Klauder, J. R.), W. H. Freeman, San Fransico, 1972.
  • G. ‘t Hooft and M. J. G. Veltman, Annales Poincaré Phys. Theor., 1974, A20, 69.
  • Goroff, M. H. and Sagnotti, A., Nucl. Phys., 1986, B266, 709.
  • Stelle, K. S., Phys. Rev., 1977, D16, 953; Tomboulis, T., Phys. Lett., 1980, B97, 77.
  • Deser, S., Kay, J. and Stelle, K. S., Phys. Rev. Lett., 1977, 38, 527; Grisaru, M. T., Van Nieuwenhuizen, P. and Vermaseren, J. A. M., Phys. Rev. Lett., 1976, 37, 1662.
  • Howe, P. S. and Stelle, K. S., Int. J. Mod. Phys., 1989, A4, 1871.
  • Arnowitt, R., Deser, S. and Misner, C. W., (ed. Witten, L.), John Wiley, New York, 1962.
  • Komar, A., In Relativity (eds Carmeli, M., Fickler, S. I. and Witten, L.), In The Dynamics of General Relativity, Plenum, New York, p. 1080.
  • Bergmann, P. G. and Komar, A., The phase space formulation of general relativity and approaches towards its quantization. In General Relativity and Gravitation (ed. Held, A.), Plenum, New York, vol. 1.
  • Ashtekar, A. and Geroch, R., Quantum theory of gravitation. Rep. Prog. Phys., 1974, 37, 1211–1256.
  • Kuchař, K., Canonical methods of quantization. In Quantum Gravity 2, A Second Oxford Symposium (eds Isham, C. J., Penrose, R. and Sciama, D. W.), Clarendon Press, Oxford, 1975.
  • Wheeler, J. A., Geometrodynamics, Academic Press, New York, 1964; In Relativity, Groups and Topology (eds DeWitt, C. M. and DeWitt, B. S.), Gordon and Breach, New York, 1963.
  • Parker, L., Creation of particles in an expanding universe. Ph D Dissertation, 1967.
  • Ford, L. H. and Wu, C. H., AIP Conf. Proc., 2008, 977, 145–159.
  • Everett, A. and Roman, T., Time Travel and Warp Drives: A Scientific Guide to Shortcuts through Time and Space, University of Chicago, Chicago, 2012.
  • Ashtekar, A., Berger, B., Isenberg, J. and MacCallaum, M. A. H. (eds), General relativity and Gravitation, A Centennial Survey, Cambridge University Press, Cambridge, 2015, part IV; see also the pre-print arXiv:1409.5823 by the editors.
  • Burgess, C. P., Living Rev. Relativity, 2004, 7, 5.
  • Porto, R. A. and Rothstein, I. Z., Phys. Rev., 2008, D78, 044013; 2010, D81, 029902.
  • Ashtekar, A., Phys. Rev. Lett., 1986, 57, 2244–2247; Phys. Rev., 1987, D36, 1587–1603.
  • Ashtekar, A. and Lewandowski, J., Class. Quant. Grav., 2004, 21, R53–R152.
  • Hellmann, F. et al. (eds), Proceedings of the Quantum Gravity and Quantum Geometry School, Zakopane, PoS (QGQGS), 2011; http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=140
  • Gambini, R. and Pullin, J., Phys. Rev. Lett., 2013, 110, 211301; Class. Quant. Grav., 2014, 31, 115003; AIP Conf. Proc., 2015, 1647, 19.
  • Alesci, E., Bianchi, E. and Rovelli, C., Class. Quant. Grav., 2009, 26, 215001; Bianchi, E., Magliaro, E. and Perini, C., Nucl. Phys., 2009, B822, 245–269C; Bianchi, E. and Ding, Y., Phys. Rev., 2012, D86, 104040.
  • Ashtekar, A. and Singh, P., Class. Quant. Grav., 2011, 28, 213008.
  • Ashtekar, A. and Barrau, A., Class. Quant. Grav. (at press).
  • Agullo, I., Phys. Rev. D, 2015, 92, 064038.
  • Agullo, I., Ashtekar, A. and Nelson, W., Phys. Rev. Lett., 2012, 109, 2513; Phys. Rev., 2013, D87, 043507; Class. Quant. Grav., 2013, 30, 085104.
  • Agullo, I. and Parker, L., Phys. Rev., 2011, D83, 063526; Agullo, I., Navarro-Salas, J. and Parker, L., JCAP, 2012, 1205, 019.

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  • Quantum General Relativity

Abstract Views: 212  |  PDF Views: 94

Authors

Abhay Ashtekar
Institute for Gravitation and the Cosmos and Physics Department, Penn State, University Park, PA 16802, United States

Abstract


After a brief historical introduction on quantum gravity as a whole, the current status of loop quantum gravity is discussed. Because of space limitation, I could only illustrate recent advances through one example - cosmology of the every early universe - and provide references for results in other main areas.

Keywords


General Relativity, Loop Quantum Gravity, Quantum Gravity.

References





DOI: https://doi.org/10.18520/cs%2Fv109%2Fi12%2F2243-2249