Quantum Entanglement and Thermodynamics of Boson-Antiboson Pair Creation Modes in the Noncommutative Bianchi I Universe

含辐射的非对易Bianchi I模型

A noncommutative Bianchi I model with radiation

该文研究与辐射耦合的非对易Bianchi I模型的动力学，通过Misner参数化、变量变换推导动力学方程并数值求解，发现其可解释宇宙加速膨胀，且演化后会趋于各向同性宇宙。

A Twisted ${\mathcal C}^{\star}$-algebra formulation of Quantum Cosmology with application to the Bianchi I model

A twisted ${\mathcal C}^\star $- algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the Uncertainty Principle for coordinates in the Planck length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I Cosmology, leads to a new set of equations that describe the quantum evolution of the universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding region…

Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space

We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in $x$, $y$ and $z$ directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are…

Generalized uncertainty principle in Bianchi type I quantum cosmology

We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

形变量子化与内蕴非交换微分几何

Deformation quantization and intrinsic noncommutative differential geometry

本文提出非交换微分几何的内蕴表述，给出协变导数、曲率及Bianchi恒等式的几何定义，证明特定条件下Ricci曲率等价，并计算球对称等距嵌入的量子涨落与曲率，表明引力量子化可重整化，最后定义准连接并证明第一Bianchi恒等式。

Rotating Bianchi type V dust models generalizing the k = -1 Friedmann model

The Einstein equations for one of the hypersurface-homogeneous rotating dust models are investigated. It is a Bianchi type V model in which one of the Killing fields is spanned on velocity and rotation (case 1.2.2.2 in the classification scheme of the earlier papers). A first integral of the field equations is found, and with a special value of this integral coordinate transformations are used to eliminate two components of the metric. The k = -1 Friedmann model is shown to be contained among the solutions in the limit of zero rotation. The field equations for the simplified metric are reduced…

Noncommutative Coherent States and Quantum Cosmology

The set of coherent states for a noncommutative quantum Bianchi I anisotropic cosmology were built to circumvent the absence of a simultaneous set of configuration observables. By extending known methods of path integrals with coherent states to their noncommutative analogues allowed us to obtain the formal expression of the propagator of the theory in terms of the covariant Husimi Q-symbol of the quantum constraint. The analysis of the equations of motion resulting from a steepest descent procedure showed the existence of solutions displaying a minimum value of the volume scaling function whi…