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- Muxin Han, Weiming Huang, Yongge Ma
- 2007

1 Abstract In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturba-tive quantum theory for Lorentzian gravitational field on four dimensional… (More)

- Muxin Han, Yongge Ma
- 2008

We introduce a Master Constraint OperatorˆM densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity. The corresponding quadratic form coincides with the one proposed by Thiemann in the master constraint programme. It is shown thatˆM is positive and symmetric, and hence has its Friedrichs self-adjoint extension. So the master… (More)

We consider the Palatini formalism of gravity with cosmological constant Λ coupled to a scalar field φ in n-dimensions. The n-dimensional Einstein equations with Λ can be derived by the variation of the coupled Palatini action provided n > 2. The Hamiltonian analysis of the coupled action is carried out by a 1 + (n − 1) decomposition of the spacetime. It… (More)

We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to 5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the underlying 5-dimensional space-time, the theory is reduced to a 4-dimensional theory where the 4-metric is coupled with… (More)

- Muxin Han, Yongge Ma
- 2008

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism… (More)

We study the properties ofˆQ[ω] operator on the kinematical Hilbert space H for canonical quantum gravity. Its complete spectrum with respect to the spin network basis is obtained. It turns out thatˆQ[ω] is diagonalized in this basis, and it is a well defined self-adjoint operator on H. The same conclusions are also tenable on the SU (2) gauge invariant… (More)

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations, hence the degeneracy of 3-metrics is not preserved by the evolution of Ashtekar's equations. As the s-knot state corresponding to this… (More)

- Han He, Yongge Ma, Xuejun Yang
- 2008

In a space-time M with a Killing vector field ξ a which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξ a gives a 3-dimensional space S. Besides the symmetry-reduced action from that of Einstein-Hilbert, an alternative action of the fields on S is also proposed which gives the same fields equations as those… (More)

- Muxin Han, Yongge Ma
- 2008

We introduce a master constraint operatorˆM densely defined in the diffeomor-phism invariant Hilbert space in loop quantum gravity, which corresponds classically to the master constraint in the programme. It is shown thatˆM is positive and symmetric, and hence has its Friedrichs self-adjoint extension. The same conclusion is tenable for an alternative… (More)

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations, hence the degeneracy of 3-metrics is not preserved by the evolution of Ashtekar's equations. As the s-knot state corresponding to this… (More)