P Renteln and L Smolin 1989 Class. Quantum Grav. 6 275 doi:10.1088/0264-9381/6/3/009
P Renteln and L Smolin
Show affiliationsThe authors present a new lattice regularisation of quantum general relativity based on Ashtekar's reformulation (1986) of Hamiltonian general relativity. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. The authors construct lattice versions of these constraints. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
04.60.Nc Lattice and discrete methods
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
83C27 Lattice gravity, Regge calculus and other discrete methods
Issue 3 (March 1989)
P Renteln and L Smolin 1989 Class. Quantum Grav. 6 275
The CMS Collaboration et al 2008 JINST 3 S08004
The CALICE collaboration et al 2008 JINST 3 P08001
Michael C. Cushing et al. 2009 ApJ 706 923
Tomaž Žagar et al 2005 New J. Phys. 7 253
M Pokorny and H U Astrom 1975 J. Phys. F: Met. Phys. 5 1327
Daniel Schaerer et al 1997 ApJ 484 L153
A. Alexandrov et al JHEP12(2009)053
Robbie C. Dohm-Palmer et al. 1998 The Astronomical Journal 116 1227
Maxim Olshanii and Vanja Dunjko 2003 New J. Phys. 5 98