arXiv subjects

Yongge Ma

Publications and source records attributed to Yongge Ma.

At least 91 records · Page 5Linked to original sources

arXiv2009

Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and effective scenario, are robust against the ambiguities. In this paper, we consider a typical quantization ambiguity arising from the quantization of the field strength of the gravitational connection. An alternative Hamiltonian constraint operator is constructed, which is shown to have the correct classical limit by the semiclassical analysis. The effective Hamiltonian incorporating higher order quantum corrections is also obtained. In the spatially flat FRW model with a massless scalar field, the classical big bang is again replaced by a quantum bounce. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect. Thus, these key features are robust against this quantization ambiguity.

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arXiv2009

Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this paper, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.

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arXiv2009

Effective Scenario of Loop Quantum Cosmology

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 correction terms may lead to significant departure from the leading order effective scenario is revealed. If the semiclassicality of the model is maintained in the large scale limit, there are great possibilities for $k=0$ Friedmann expanding universe to undergo a collapse in the future due to the quantum gravity effect. Thus the quantum bounce and collapse may contribute a cyclic universe in the new scenario.

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arXiv2007

State-Relevant Maxwell's Equation from Kaluza-Klein Theory

We study a five-dimensional perfect fluid coupled with Kaluza-Klein (KK) gravity. By dimensional reduction, a modified form of Maxwell's equation is obtained, which is relevant to the equation of state of the source. Since the relativistic magnetohydrodynamics (MHD) and the 3-dimensional formulation are widely used to study space matter, we derive the modified Maxwell's equations and relativistic MHD in 3+1 form. We then take an ideal Fermi gas as an example to study the modified effect, which can be visible under high density or high energy condition, while the traditional Maxwell's equation can be regarded as a result in the low density and low temperature limit. We also indicate the possibility to test the state-relevant effect of KK theory in a telluric laboratory.

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arXiv2007

Five-dimensional PPN formalism and experimental test of Kaluza-Klein theory

The parametrized post Newtonian formalism for 5-dimensional metric theories with a compact extra dimension is developed. The relation of the 5-dimensional and 4-dimensional formulations is then analyzed, in order to compare the higher dimensional theories of gravity with experiments. It turns out that the value of post Newtonian parameter $γ$ in the reduced 5-dimensional Kaluza-Klein theory is two times smaller than that in 4-dimensional general relativity. The departure is due to the existence of an extra dimension in the Kaluza-Klein theory. Thus the confrontation between the reduced 4-dimensional formalism and Solar system experiments raises a severe challenge to the classical Kaluza-Klein theory.

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arXiv2007

Fundamental Structure of Loop Quantum Gravity

In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background independent quantum gauge theories. There is no divergence within this background independent and diffeomorphism invariant quantization programme of matter coupled to gravity.

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arXiv2006

Semi-classical States in Homogeneous Loop Quantum Cosmology

Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semi-classical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semi-classical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.

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arXiv2006

Master Constraint Operator in Loop Quantum Gravity

We introduce a master constraint operator $\hat{\mathbf{M}}$ densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity, which corresponds classically to the master constraint in the programme. It is shown that $\hat{\mathbf{M}}$ is positive and symmetric, and hence has its Friedrichs self-adjoint extension. The same conclusion is tenable for an alternative master operator $\hat{\mathbf{M'}}$, whose quadratic form coincides with the one proposed by Thiemann. So the master constraint programme for loop quantum gravity can be carried out in principle by employing either of the two operators.

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arXiv2006

Dynamics of Scalar Field in Polymer-like Representation

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 invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are 1-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background independent and diffeomorphism invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism invariant Hilbert space.

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arXiv2005

Palatini Formalism of 5-Dimensional Kaluza-Klein Theory

The Einstein field equations can be derived in $n$ dimensions ($n>2$) by the variations of the Palatini action. The Killing reduction of 5-dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are preserved by the Killing vector field. A Palatini formalism of 4-dimensional action for gravity coupled to a vector field and a scalar field is obtained, which gives exactly the same fields equations in Kaluza-Klein theory.

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arXiv2005

Hamiltonian analysis of $n$-dimensional Palatini gravity with matter

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 turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of $Λ$ and $ϕ$. While, the $n$-dimensional Palatini action could not give a connection dynamics formalism directly.

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arXiv2005

5-dimensional Brans-Dicke Theory and Cosmic Acceleration

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 spacetime, the theory is reduced to a 4-dimensional theory where the 4-metric is coupled with two scalar fields. The cosmological implication of this reduced theory is then studied in the Robertson-Walker model. It turns out that the two scalar fields may account naturally for the present accelerated expansion of our universe. The observational restriction of the reduced cosmological model is also analyzed.

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arXiv2005

5-Dimensional Kaluza-Klein Theory with a Source

A free test particle in 5-dimensional Kaluza-Klein spacetime will show its electricity in the reduced 4-dimensional spacetime when it moves along the fifth dimension. In the light of this observation, we study the coupling of a 5-dimensional dust field with the Kaluza-Klein gravity. It turns out that the dust field can curve the 5-dimensional spacetime in such a way that it provides exactly the source of the electromagnetic field in the 4-dimensional spacetime after the dimensional reduction.

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arXiv2003

Killing Reduction of 5-Dimensional Spacetimes

In a 5-dimensional spacetime ($M,g_{ab}$) 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 4-dimensional space $S$. The reduction of ($M,g_{ab}$) is studied in the geometric language, which is a generalization of Geroch's method for the reduction of 4-dimensional spacetime. A 4-dimensional gravity coupled to a vector field and a scalar field on $S$ is obtained by the reduction of vacuum Einstein's equations on $M$, which gives also an alternative description of the 5-dimensional Kaluza-Klein theory. Besides the symmetry-reduced action from the Hilbert action on $M$, an alternative action of the fields on $S$ is also obtained, the variations of which lead to the same fields equations as those reduced from the vacuum Einstein equation on $M$.

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arXiv2003

Actions for Vacuum Einstein's Equation with a Killing Symmetry

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-dimension 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 reduced from the vacuum Einstein equation on $M$.

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arXiv2002

Quantization of static space-times

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum theory which actually describes quantized static space-times. The Kinematical Hilbert space is the product of the Hilbert space of gravity with that of imaginary scalar fields. It turns out that the Hamiltonian constraint of the 2+1 model corresponds to a densely defined operator in the underlying Hilbert space, and hence it is finite without renormalization. As a new point of view, this quantized model might shed some light on a few physical problems concerning quantum gravity.

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arXiv2000

$\hat{Q}$ operator for canonical quantum gravity

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

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arXiv2000

Classical Geometry from a Physical State in Canonical Quantum Gravity

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 weave is shown to solve all the quantum constraints in loop quantum gravity, a physical state in canonical quantum gravity is related to the familiar classical geometry.

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