Kinematical Hilbert spaces for fermionic and Higgs quantum field theories

Classical and Quantum Gravity

Volumn 15, Issue 6, 1998, Pages 1487-1512

  Thiemann, T ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032361785     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/15/6/006     Document Type: Article

References (36)

1. Glimm J and Jaffe A 1987 Quantum Physics (New York: Springer)
2. Yamasaki Y 1984 Measures on Infinite Dimensional Spaces (Singapore: World Scientific)
3. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Quantization for diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 519-51
4. Ashtekar A and Isham C J 1992 Class. Quantum Grav. 9 1433
5. Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy C* algebras Knots and Quantum Gravity ed J Baez (Oxford: Oxford University Press)
6. Ashtekar A and Lewandowski J 1995 Differential geometry on the space of connections via graphs and projective limits J. Geo. Phys. 17 191
7. Ashtekar A and Lewandowski J 1995 J. Math. Phys. 36 2170
8. Marolf D and Mourão J M 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606
9. 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)
10. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1997 SU(N) Yang-Mills theory in two dimensions: a complete solution J. Math. Phys. 38 5453
11. Higuchi A 1991 Class. Quantum Grav. 8 1983
12. Higuchi A 1991 Class. Quantum Grav. 8 2023
13. Marolf D 1995 The spectral analysis inner product for quantum gravity Proc. VIIth Marcel-Grossman Conf. ed R Ruffini and M Keiser (Singapore: World Scientific) Marolf D 1995 Class. Quantum Grav. 12 1199 Marolf D 1995 Almost ideal clocks in quantum cosmology: a brief derivation of time Class. Quantum Grav. 12 2469
14. Marolf D 1995 The spectral analysis inner product for quantum gravity Proc. VIIth Marcel-Grossman Conf. ed R Ruffini and M Keiser (Singapore: World Scientific) Marolf D 1995 Class. Quantum Grav. 12 1199 Marolf D 1995 Almost ideal clocks in quantum cosmology: a brief derivation of time Class. Quantum Grav. 12 2469
15. Marolf D 1995 The spectral analysis inner product for quantum gravity Proc. VIIth Marcel-Grossman Conf. ed R Ruffini and M Keiser (Singapore: World Scientific) Marolf D 1995 Class. Quantum Grav. 12 1199 Marolf D 1995 Almost ideal clocks in quantum cosmology: a brief derivation of time Class. Quantum Grav. 12 2469
16. Ashtekar A 1986 Phys. Rev. Lett. 57 2244 Ashtekar A 1987 Phys. Rev. D 36 1587
17. Ashtekar A 1986 Phys. Rev. Lett. 57 2244 Ashtekar A 1987 Phys. Rev. D 36 1587
18. Barbero F 1995 Phys. Rev. D 51 5507
19. Morales-Tecótl H and Rovelli C 1995 Phys. Rev. Lett. 72 3642-5 Morales-Tecótl H and Rovelli C 1995 Nucl. Phys. B 331 325-61
20. Morales-Tecótl H and Rovelli C 1995 Phys. Rev. Lett. 72 3642-5 Morales-Tecótl H and Rovelli C 1995 Nucl. Phys. B 331 325-61
21. Thiemann T 1996 Anomaly-free formulation of non-perturbative, four-dimensional, Lorentzian quantum gravity Phys. Lett. 380B 257-64 Thiemann T 1996 Phys. Lett. 380N 257-64
22. Thiemann T 1996 Anomaly-free formulation of non-perturbative, four-dimensional, Lorentzian quantum gravity Phys. Lett. 380B 257-64 Thiemann T 1996 Phys. Lett. 380N 257-64
23. 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
24. 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
25. 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
26. Thiemann T 1998 Quantum spin dynamics (QSD): IV. 2 + 1 Euclidean quantum gravity as a model to test 3 + 1 Lorentzian quantum gravity Class. Quantum Grav. 15 1249-80
27. Thiemann T 1998 Quantum spin dynamics (QSD). VI. Quantum Poincaré algebra and a quantum positivity of energy theorem for canonical quantum gravity Class. Quantum Grav. 15 1463-85
28. Baez J and Krasnov K 1998 Quantization of diffeomorphism invariant theories with fermions J. Math. Phys. 39 1251
29. 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
30. Jacobson T 1988 Fermions in canonical gravity Class. Quantum Grav. 5 L143-8
31. Choquet-Bruhat Y and DeWitt-Morette C 1989 Analysis, Manifolds and Physics Part II: 92 Applications (Amsterdam: North-Holland)
32. DeWitt B 1992 Supermanifolds (Cambridge: Cambridge University Press)
33. Ashtekar A and Lewandowski J Quantum theory of geometry II: volume operators Preprint gr-qc/9711031
34. Rovelli C and Smolin L 1995 Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 743 (erratum)
35. Rovelli C and Smolin L 1995 Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 743 (erratum)
36. Ashtekar A, Corichi A, Lewandowski J and Zapata J-A 1997 Quantum theory of geometry III: non-commutativity of Riemannian structures (in preparation)