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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)

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)

- Xiangdong Zhang, Yongge Ma
- Physical review letters
- 2011

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure… (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)

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)

- You Ding, Yongge Ma, Jinsong Yang
- Physical review letters
- 2009

Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus obtained, which incorporates also the next to leading order quantum corrections. The possibility that the higher order… (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)

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)

- Yongge Ma
- 1999

We show from one-loop quantum gravity and statistical thermodynamics that the thermodynamics of quantum foam in flat space-time and Schwarzschild space-time is exactly the same as that of Hawking-Unruh radiation in thermal equilibrium. This means we show unambiguously that Hawking-Unruh thermal radiation should contain thermal gravitons or the contribution… (More)