Quantum spin dynamics (QSD): IV. 2 + 1 Euclidean quantum gravity as a model to test 3 + 1 Lorentzian quantum gravity

Classical and Quantum Gravity

Volumn 15, Issue 5, 1998, Pages 1249-1280

  Thiemann, T ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032369978     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/15/5/011     Document Type: Article

References (30)

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6. Thiemann T 1996 Phys. Lett. 380B 257-64 Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quantum Grav. 15 839-73 Thiemann T 1998 Quantum spin dynamics (QSD): II. The kernel of the Wheeler-DeWitt constraint operator Class. Quantum Grav. 15 875-905
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15. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433 Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170 Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 A manifestly gauge invariant approach to quantum theories of gauge fields Geometry of Constrained Dynamical Systems ed J Charap (Cambridge: Cambridge University Press) Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T Constructive quantum gauge field theory in two space-time dimensions CGPG Preprint
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17. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433 Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170 Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 A manifestly gauge invariant approach to quantum theories of gauge fields Geometry of Constrained Dynamical Systems ed J Charap (Cambridge: Cambridge University Press) Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T Constructive quantum gauge field theory in two space-time dimensions CGPG Preprint
18. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433 Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170 Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 A manifestly gauge invariant approach to quantum theories of gauge fields Geometry of Constrained Dynamical Systems ed J Charap (Cambridge: Cambridge University Press) Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T Constructive quantum gauge field theory in two space-time dimensions CGPG Preprint
19. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433 Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170 Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 A manifestly gauge invariant approach to quantum theories of gauge fields Geometry of Constrained Dynamical Systems ed J Charap (Cambridge: Cambridge University Press) Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T Constructive quantum gauge field theory in two space-time dimensions CGPG Preprint
20. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433 Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press) Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191 Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170 Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606 Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1994 A manifestly gauge invariant approach to quantum theories of gauge fields Geometry of Constrained Dynamical Systems ed J Charap (Cambridge: Cambridge University Press) Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T Constructive quantum gauge field theory in two space-time dimensions CGPG Preprint
21. Rovelli C and Smolin L 1995 Discreteness of volume and area in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum) Ashtekar A and Lewandowski J 1998 Quantum geometry II: volume operators Preprint gr-qc/9711031 Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6 De Pietri R and Rovelli C 1996 Geometry eigenvalues and scalar product from recoupling theory in loop quantum theory Phys. Rev. D 54 2664
22. Rovelli C and Smolin L 1995 Discreteness of volume and area in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum) Ashtekar A and Lewandowski J 1998 Quantum geometry II: volume operators Preprint gr-qc/9711031 Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6 De Pietri R and Rovelli C 1996 Geometry eigenvalues and scalar product from recoupling theory in loop quantum theory Phys. Rev. D 54 2664
23. Rovelli C and Smolin L 1995 Discreteness of volume and area in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum) Ashtekar A and Lewandowski J 1998 Quantum geometry II: volume operators Preprint gr-qc/9711031 Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6 De Pietri R and Rovelli C 1996 Geometry eigenvalues and scalar product from recoupling theory in loop quantum theory Phys. Rev. D 54 2664
24. Rovelli C and Smolin L 1995 Discreteness of volume and area in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum) Ashtekar A and Lewandowski J 1998 Quantum geometry II: volume operators Preprint gr-qc/9711031 Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6 De Pietri R and Rovelli C 1996 Geometry eigenvalues and scalar product from recoupling theory in loop quantum theory Phys. Rev. D 54 2664
25. Rovelli C and Smolin L 1995 Discreteness of volume and area in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum) Ashtekar A and Lewandowski J 1998 Quantum geometry II: volume operators Preprint gr-qc/9711031 Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6 De Pietri R and Rovelli C 1996 Geometry eigenvalues and scalar product from recoupling theory in loop quantum theory Phys. Rev. D 54 2664
26. Thiemann T Complete formula for the matrix elements of the volume operator in canonical quantum gravity Harvard University Preprint HUTMP-96/B-353, gr-qc/9606091 (J. Math. Phys. to be published)
27. Thiemann T 1998 Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories Class. Quantum Grav. 15 1281-314
28. Thiemann T A length operator for canonical quantum gravity Harvard University Preprint HUTMP-96/B-354, gr-qc/9606092
29. Thiemann T 1998 Quantum spin dynamics (QSD): III. Quantum constraint algebra and physical scalar product in quantum general relativity Class. Quantum Grav. 15 1207-47
30. Marolf D, Mourão J and Thiemann T 1997 The status of diffeomorphism superselection in Euclidean 2 + 1 gravity J. Math. Phys. 38 4730