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Approaches to Quantum Gravity

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<strong>Quantum</strong> Regge calculus 377[52] M. Leh<strong>to</strong>, H. B. Nielsen & M. Ninomiya, Diffeomorphism symmetry in simplicialquantum gravity, Nucl. Phys. B, 272 (1986) 228–52.[53] R. Loll, Discrete approaches <strong>to</strong> quantum gravity in four dimensions, Living Rev.Rel., 1 (1998) 13.[54] J. Louko & P. A. Tuckey, Regge calculus in anisotropic quantum cosmology, Class.<strong>Quantum</strong> Grav., 9 (1991) 41–67.[55] F. Lund & T. Regge, Simplicial approximation <strong>to</strong> some homogeneous cosmologies(1974), unpublished.[56] P. Menotti & R. P. Peirano, Functional integral for Regge gravity, Nucl. Phys. B.Proc. Suppl., 57 (1997) 82–90.[57] W. A. Miller, The geometrodynamic content of the Regge equations as illuminatedby the boundary of a boundary principle, Found. Phys., 16 (1986) 143–69.[58] G. Ponzano & T. Regge, Semiclassical limit of Racah coefficients, in Spectroscopicand Group Theoretical Methods in Physics, eds. F. Block, S. G. Cohen, A. DeShalit,S. Sambursky & I. Talmi, pp. 1–58 (Amsterdam, North-Holland, 1968).[59] T. Regge, General relativity without coordinates, Nuovo Cimen<strong>to</strong>, 19 (1961) 558–71.[60] T. Regge & R. M. Williams, Discrete structures in gravity, J. Math. Phys., 41 (2000)3964–84.[61] H. C. Ren, Matter fields in lattice gravity. Nucl. Phys. B, 301 (1988) 661–84.[62] J. Riedler, W. Beirl, E. Bittner, A. Hauke, P. Homolka & H. Markum, Phasestructure and gravi<strong>to</strong>n propaga<strong>to</strong>rs in lattice formulations of four-dimensionalquantum gravity. Class. <strong>Quantum</strong> Grav., 16 (1999) 1163–73.[63] M. Rocek & R. M. Williams, Introduction <strong>to</strong> quantum Regge calculus, in <strong>Quantum</strong>Structure of Space and Time, eds. M. J. Duff & C. J. Isham, pp. 105–16 (Cambridge,Cambridge University Press, 1982).[64] M. Rocek & R. M. Williams, The quantisation of Regge calculus, Z. Phys. C, 21(1984) 371–81.[65] H. Römer & M. Zähringer, Functional integration and the diffeomorhism group inEuclidean lattice quantum gravity, Class. <strong>Quantum</strong> Grav., 3 (1986) 897–910.[66] K. Schleich & D. M. Witt, Generalized sums over his<strong>to</strong>ries for quantum gravity II:simplicial conifolds, Nucl. Phys. B, 402 (1983) 469–528.[67] P. A. Tuckey, <strong>Approaches</strong> <strong>to</strong> 3+1 Regge calculus, Ph. D. thesis, University ofCambridge (1988).[68] V. G. Turaev & O. Y. Viro, State sum invariants of 3-manifolds and quantum6j-symbols. Topology, 31 (1992) 865–902.[69] M. Veltman, in Methods in Field Theory, Les Houches lecture Notes Series, SessionXXVIII (Amsterdam, North-Holland, 1975).[70] R. M. Williams, <strong>Quantum</strong> Regge calculus in the Lorentzian domain and itsHamil<strong>to</strong>nian formulation, Class. <strong>Quantum</strong> Grav., 3 (1986) 853–69.[71] R. M. Williams & P. A. Tuckey, Regge calculus: a brief review and bibliography,Class. <strong>Quantum</strong> Grav., 9 (1992) 1409–22.

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