Action of the Diffeomorphism Constraint in the Extended Loop Representation of Quantum Gravity

SHAO ChangGui; XIAO JunHua; SHAO Liang; PAN GuiJun; CHEN ZhongQiu

Chinese Physics C> 2000, Vol. 24> Issue(5) : 390-399

Action of the Diffeomorphism Constraint in the Extended Loop Representation of Quantum Gravity

Institute of Theoretical Physics of Hubei University, Wuhan, 430062 China

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Abstract：
By a different way, we particularized the action of the diffeomorphism constraint (D-constraint) on the abstract wave function in the extended loop representation to the action in the loop representation. Using the two-point propagator of Chern-Simons theory as the basic blocks of quantum gravity states, we constructed the extended knot invariant gravity states (*φ_G)ⁿ that which satisfied with the homogeneous D-constraint. For the states of n=1,2, we demonstrated a detailed proof, To the states of n>2, we gave a general identification.

References

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Ashtekar A. Phys. Rev. Lett.,1986,57:2244;Phys. Rev.,1987,D36:1587[2] Rovelli C,Smolin L.Nucl. Phys.,1990,B331:80[3] Markopoulou F, Smolin L. Nucl. Phys.,1997,B508;409[4] Di Bartolo C,Gambini R,Griego J. Phys. Rev.,1995, D51:502[5] Di Bartolo C,Gambini R,Griego J. et al. Phys. Rev. Lett.,1994, 72:3638[6] Griego J. Nucl. Phys.,1996, 8467:332[7] Rovelli C,Smolin L. Phys. Rev. Lett.,1988, 61:1155[8] Bnigmann B,Gambini R,Pullin J. Phys. Rev. Lett.,1992, 68:431

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SHAO ChangGui, XIAO JunHua, SHAO Liang, PAN GuiJun and CHEN ZhongQiu. Action of the Diffeomorphism Constraint in the Extended Loop Representation of Quantum Gravity[J]. Chinese Physics C, 2000, 24(5): 390-399.

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Received: 1999-03-02
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Action of the Diffeomorphism Constraint in the Extended Loop Representation of Quantum Gravity

Corresponding author: SHAO ChangGui,

Institute of Theoretical Physics of Hubei University, Wuhan, 430062 China

Received Date: 1999-03-02
Accepted Date: 1900-01-01
Available Online: 2000-04-05

Abstract: By a different way, we particularized the action of the diffeomorphism constraint (D-constraint) on the abstract wave function in the extended loop representation to the action in the loop representation. Using the two-point propagator of Chern-Simons theory as the basic blocks of quantum gravity states, we constructed the extended knot invariant gravity states (*φ_G)ⁿ that which satisfied with the homogeneous D-constraint. For the states of n=1,2, we demonstrated a detailed proof, To the states of n>2, we gave a general identification.