Geodesic
Lorentz-Covariant Loop Quantum Gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 363-380 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We review the Lorentz-covariant approach to loop quantum gravity. This approach solves the Immirzi parameter problem occurring in the standard loop approach based on the $SU(2)$ gauge group. We show that there exists a unique loop quantization preserving all the classical symmetries at the quantum level and that the results obtained with it, such as the area operator spectrum, are independent of the Immirzi parameter. The standard $SU(2)$ approach violates the diffeomorphism invariance and is therefore an incorrect quantization of gravity.
Keywords: loop gravity, BRST path integral.
Mots-clés : canonical quantization 
@article{TMF_2004_139_3_a1,
     author = {S. Yu. Alexandrov},
     title = {Lorentz-Covariant {Loop} {Quantum} {Gravity}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {363--380},
     year = {2004},
     volume = {139},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a1/}
}
TY  - JOUR
AU  - S. Yu. Alexandrov
TI  - Lorentz-Covariant Loop Quantum Gravity
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2004
SP  - 363
EP  - 380
VL  - 139
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a1/
LA  - ru
ID  - TMF_2004_139_3_a1
ER  - 
%0 Journal Article
%A S. Yu. Alexandrov
%T Lorentz-Covariant Loop Quantum Gravity
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2004
%P 363-380
%V 139
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a1/
%G ru
%F TMF_2004_139_3_a1
S. Yu. Alexandrov. Lorentz-Covariant Loop Quantum Gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 363-380. http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a1/

[1] C. Rovelli, L. Smolin, Phys. Rev. Lett., 61 (1988), 1155 ; Nucl. Phys. B, 331 (1990), 80 | DOI | MR | DOI | MR

[2] M. Gaul, C. Rovelli, “Loop quantum gravity and the meaning of diffeomorphism invariance”, Towards Quantum Gravity, Proc. of the 35th Intern. Winter School on Theoretical Physics (Polanica, Poland, 2–11 February 1999), Lect. Notes Phys., 541, ed. J. Kowalski-Glikman, Springer, Berlin, 2000, 277 ; E-print gr-qc/9910079 | DOI | MR | Zbl

[3] C. Rovelli, L. Smolin, Nucl. Phys. B, 442 (1995), 593 ; A. Ashtekar, J. Lewandowski, Class. Q Grav., 14 (1997), 55 | DOI | MR | Zbl | DOI | MR

[4] R. Loll, Phys. Rev. Lett., 75 (1995), 3048 ; R. DePietri, C. Rovelli, Phys. Rev. D, 54 (1996), 2664 ; J. Lewandowski, Class. Q Grav., 14 (1997), 71 | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl

[5] C. Rovelli, Phys. Rev. Lett., 77 (1996), 3288 ; A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, Phys. Rev. Lett., 80 (1998), 904 | DOI | MR | Zbl | DOI | MR | Zbl

[6] J. F. Barbero, Phys. Rev. D, 49 (1994), 6935 | DOI | MR

[7] A. Ashtekar, Phys. Rev. Lett., 57 (1986), 2244 ; Phys. Rev. D, 36 (1987), 1587 | DOI | MR | DOI | MR

[8] G. Immirzi, Nucl. Phys. Proc. Suppl., 57 (1997), 65 | DOI | MR | Zbl

[9] S. Alexandrov, Class. Q Grav., 17 (2000), 4255 | DOI | MR | Zbl

[10] S. Alexandrov, D. Vassilevich, Phys. Rev. D, 64 (2001), 044023 | DOI | MR

[11] S. Alexandrov, Phys. Rev. D, 65 (2002), 024011 | DOI | MR

[12] S. Alexandrov, Phys. Rev. D, 66 (2002), 024028 | DOI | MR

[13] S. Alexandrov, E. R. Livine, Phys. Rev. D, 67 (2003), 044009 ; E-print gr-qc/0209105 | DOI | MR

[14] A. Ashtekar, Lectures on Non-Perturbative Canonical Gravity, World Scientific, Singapore, 1991 | MR

[15] T. Thiemann, Class. Q Grav., 13 (1996), 1383 | DOI | MR | Zbl

[16] A. Ashtekar, J. D. Romano, R. S. Tate, Phys. Rev. D, 40 (1989), 2572 ; G. Immirzi, Class. Q Grav., 10 (1993), 2347 | DOI | MR | DOI | MR

[17] A. Ashtekar, J. Lewandowski, J. Math. Phys., 36 (1995), 2170 | DOI | MR | Zbl

[18] C. Rovelli, L. Smolin, Phys. Rev. D, 52 (1995), 5743 ; J. Baez, “Spin networks in nonperturbative quantum gravity”, The interface of knots and physics, ed. L. Kauffman, American Mathematical Society, Providence, Rhode Island, 1996, 167 ; E-print gr-qc/9504036 | DOI | MR | DOI | MR | Zbl

[19] C. Rovelli, T. Thiemann, Phys. Rev. D, 57 (1998), 1009 | DOI | MR

[20] S. Holst, Phys. Rev. D, 53 (1996), 5966 | DOI | MR

[21] E. S. Fradkin, G. A. Vilkovisky, Phys. Lett. B, 55 (1975), 244 ; I. A. Batalin, G. A. Vilkovisky, Phys. Lett. B, 69 (1977), 309 ; E. S. Fradkin, T. E. Fradkina, Phys. Lett. B, 72 (1978), 343 | DOI | MR | DOI | DOI

[22] M. Henneaux, Phys. Rep., 126 (1985), 1 | DOI | MR

[23] S. Alexandrov, I. Grigentch, D. Vassilevich, Class. Q Grav., 15 (1998), 573 | DOI | MR | Zbl

[24] S. Yu. Alexandrov, D. V. Vassilevich, Phys. Rev. D, 58 (1998), 124029 | DOI | MR

[25] J. W. Barrett, L. Crane, Class. Q Grav., 17 (2000), 3101 ; A. Perez, C. Rovelli, Phys. Rev. D, 63 (2001), 041501 ; 64, 064002 ; D. Oriti, Rep. Progr. Phys., 64 (2001), 1489 | DOI | MR | Zbl | DOI | MR | DOI | MR | DOI | MR