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

  • 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 (*φG)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.
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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.
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. shu
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Received: 1999-03-02
Revised: 1900-01-01
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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

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 (*φG)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.

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