Quantum Gravity

328 REFERENCESAshtekar, A. and Lewandowski, J. (1998). Quantum theory of geometry II:volume operators. Adv. Theor. Math. Phys., 1, 388-429.Ashtekar, A. and Lewandowski, J. (2004). Background independent quantumgravity: a status report. Class. Quantum Grav., 21, R53–152.Ashtekar, A. and Pierri, M. (1996). Probing quantum gravity through exactlysoluble midi-superspaces I. J. Math. Phys., 37, 6250–70.Ashtekar, A., Baez J., Corichi, A., and Krasnov, K. (1998). Quantum geometryand black hole entropy. Phys. Rev. Lett., 80, 904–7.Ashtekar, A., Bojowald, M., and Lewandowski, L. (2003). Mathematical structureof loop quantum cosmology. Adv. Theor. Math. Phys., 7, 233–68.Ashtekar, A., Krasnov, K., and Baez, J. (2000). Quantum geometry of isolatedhorizons and black hole entropy. Adv. Theor. Math. Phys., 4, 1–94.Ashtekar, A., Marolf, D., and Mourão, J. (1994). Integration on the space ofconnections modulo gauge transformations. In Proc. Cornelius Lanczos Int.Centenary Conf. (ed. J. D. Brown et al.), pp. 143–60. SIAM, Philadelphia.Ashtekar, A., Pawlowski, T., and Singh, P. (2006). Quantum nature of the bigbang: Improved dynamics. Phys. Rev. D, 74, 084003 [23 pages].Audretsch, J., Hehl, F. W., and Lämmerzahl, C. (1992). Matter wave interferometryand why quantum objects are fundamental for establishing a gravitationaltheory. In Relativistic gravity research (ed. J. Ehlers and G. Schäfer),pp. 368–407. Lecture Notes in Physics 410. Springer, Berlin.Baierlein, R. F., Sharp, D. H., and Wheeler. J. A. (1962). Three-dimensionalgeometry as carrier of information about time. Phys. Rev., 126, 1864–65.Bañados, M., Teitelboim, C., and Zanelli, J. (1992). The black hole in threedimensionalspace–time. Phys. Rev. Lett., 69, 1849–51.Banks, T. (1985). TCP, quantum gravity, the cosmological constant and allthat. Nucl. Phys. B, 249, 332–60.Banks, T., Fischler, W., Shenker, S. H., and Susskind, L. (1997). M theory asa matrix model: a conjecture. Phys. Rev. D, 55, 5112–28.Barbero, J. F. (1995). Real Ashtekar variables for Lorentzian space–times. Phys.Rev. D, 51, 5507–10.Barbour, J. B. (1986). Leibnizian time, Machian dynamics, and quantum gravity.In Quantum concepts in space and time (ed. R. Penrose and C. J. Isham),pp. 236–46. Oxford University Press, Oxford.Barbour, J. B. (1989). Absolute or relative motion? Vol. 1: The discovery ofdynamics. Cambridge University Press, Cambridge.Barbour, J. B. (1993). Time and complex numbers in canonical quantum gravity.Phys. Rev. D, 47, 5422–9.Barbour, J. B. (1994). The timelessness of quantum gravity: I. The evidencefrom the classical theory. Class. Quantum Grav., 11, 2853–73.Barbour, J. B. and Bertotti, B. (1982). Mach’s principle and the structure ofdynamical theories. Proc. R. Soc. Lond. A, 382, 295–306.Barbour, J. B., Foster, B., and Ó Murchadha, N. (2002). Relativity withoutrelativity. Class. Quantum Grav., 19, 3217–48.