Classical geometry from a physical state in canonical quantum gravity

Ma, Yongge; Ling, Yi

doi:10.1103/physrevd.62.064030

Cited by 8 publications

(5 citation statements)

References 32 publications

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“…On the other hand, there is no coupling between N c and ν, so there is no canonical seesaw mechanism available for m ν . As shown previously [6,7], there are in general three active and two sterile neutrinos in these E 6 models. They may acquire masses through their mixing with the extra neutral fermions (which are also leptons) at the TeV scale.…”

Section: Introductionsupporting

confidence: 77%

“…If there is new physics at the TeV scale, it should be such that the above two properties are maintained. It has now been shown [4] that assuming the extended gauge symmetry to be a subgroup of the superstring-inspired E 6 , the success of leptogenesis requires it to be either SU (3) [5,6] or SU(3) C × SU(2) L × U(1) Y × U(1) N [7,8]. Only these two gauge groups allow the superfield N c to have zero quantum numbers with 3 Three recent proposals regarding the origin of neutrino mass but not baryogenesis are exceptions to this general rule: the models with enlarged Higgs Sector [2] and the models of bilinear R-parity breaking [3].…”

Section: Introductionmentioning

confidence: 99%

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Three active and two sterile neutrinos in anE₆model of diquark baryogenesis

Raidal

2001

J. Phys. G: Nucl. Part. Phys.

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In the U (1) N extension of the supersymmetric standard model with E 6 particle content, the heavy singlet superfield N may decay into a quark and a diquark as well as an antiquark and an antidiquark, thus creating a baryon asymmetry of the Universe. We show how the three doublet and two singlet neutrinos in this model acquire mass from physics at the TeV scale without the benefit of using N as a heavy right-handed neutrino. Specifically, the active neutrinos get masses via the bilinear term µLX c which conserves R-parity, and via the nonzero masses of the sterile neutrinos. We predict fixed properties of the extra Z ′ boson, as well as the new lepton doublets X and X c , and the observation of diquark resonances at hadron colliders in this scenario.

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Section: Introductionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Three active and two sterile neutrinos in anE₆model of diquark baryogenesis

Raidal

2001

J. Phys. G: Nucl. Part. Phys.

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“…is arbitrary. These regions do not contribute to the construction of the operator, since the commutator terms like Â(s i ( )), VU v( ) s,c would vanish for all tetrahedron in the regions (13).…”

Section: Quantization Of the Hamiltonianmentioning

confidence: 99%

“…One can even solve the Gaussian and diffeomorphism constraints to arrive at a diffeomorphism-invariant Hilbert space [8]. Certain geometrical operators are shown to have discrete spectra in the kinematical Hilbert space [9][10][11][12][13]. However, some important elements in this approach are not yet understood.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a scalar field in a polymer-like representation

Han¹,

Ma²

2006

Class. Quantum Grav.

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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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“…There is only 1-dimensional geometry living on these graphs, so the quantum geometry is polymer-like object. When one increases the amount of edges and graphs such that the graphs are densely distributed in Σ, the quantum state is highly excited and the quantum geometry can weave the classical smooth one [33][1] [99]. Because of this picture, the quantum kinematical representation which we obtain is also called polymer representation for backgroundindependent quantum geometry.…”

Section: • Kinematical Vacuum and Polymer Representationmentioning

confidence: 99%

Fundamental Structure of Loop Quantum Gravity

Han

Huang

2007

Int. J. Mod. Phys. D

Self Cite

245

277

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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, nonperturbative quantum theory for Lorentzian gravitational field on four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete at fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory.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-IshamLewandowski 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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Classical geometry from a physical state in canonical quantum gravity

Cited by 8 publications

References 32 publications

Three active and two sterile neutrinos in anE₆model of diquark baryogenesis

Three active and two sterile neutrinos in anE₆model of diquark baryogenesis

Dynamics of a scalar field in a polymer-like representation

Fundamental Structure of Loop Quantum Gravity

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Classical geometry from a physical state in canonical quantum gravity

Cited by 8 publications

References 32 publications

Three active and two sterile neutrinos in anE6model of diquark baryogenesis

Three active and two sterile neutrinos in anE6model of diquark baryogenesis

Dynamics of a scalar field in a polymer-like representation

Fundamental Structure of Loop Quantum Gravity

Contact Info

Product

Resources

About

Three active and two sterile neutrinos in anE₆model of diquark baryogenesis

Three active and two sterile neutrinos in anE₆model of diquark baryogenesis