Kinematical Foundations of Loop Quantum Cosmology

Uniqueness of Measures in Loop Quantum Cosmology

In a paper of Ashtekar and Campiglia, residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations w.r.t. the extended $\mathbb{R}$-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space $\mathbb{R}_\mathrm{Bohr}$ as well as on the Fleischhack one. Thus, in both situation, the same condition singles out the standard kinematical Hi…

Kinematical uniqueness of homogeneous isotropic LQC

In a paper by Ashtekar and Campiglia, invariance under volume preserving residual diffeomorphisms has been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). In this paper, we use invariance under all residual diffeomorphisms to single out the standard kinematical Hilbert space of homogeneous isotropic LQC for both the standard configuration space $\mathbb{R}_{\mathrm{Bohr}}$, as well as for the Fleischhack one $\mathbb{R} \sqcup \mathbb{R}_{\mathrm{Bohr}}$. We first determine the scale invariant Radon measures on th…

关于对称相对论模型的几何与运动学基础：洛伦兹变换与时间膨胀

On the Geometrical and Kinematical Foundations of the Symmetric Relativity Model: Lorentz Transformation and Time Dilation

研究相对论运动学基础，通过放宽单向光速假设，采用基于双向光速的框架，证明能恢复经典洛伦兹变换等，引入运动学对称模型，得出相关效应及度规结构，且往返可观测量在规范变换下不变。

Projective Structures in Loop Quantum Cosmology

Projective structures have successfully been used for the construction of measures in the framework of loop quantum gravity. In the present paper, we establish such structures for the configuration space $\mathbb{R}\sqcup \mathbb{R}_{\mathbb{Bohr}}$, recently introduced in the context of homogeneous isotropic loop quantum cosmology. In contrast to the traditional space $\mathbb{R}_{\mathbb{Bohr}}$, the first one is canonically embedded into the quantum configuration space of the full theory. In particular, for the embedding of states into a corresponding symmetric sector of loop quantum gravit…

Schrödinger联络：从数学基础到Yano-Schrödinger宇宙学

Schrödinger Connections: From Mathematical Foundations Towards Yano-Schrödinger Cosmology

本文建立Schrödinger联络的无坐标几何理论，推广Raychaudhuri与Sachs方程，构建度量及度量-仿射引力理论，并给出与观测和ΛCDM比较的宇宙学模型。

Foundations of quantum physics V. Coherent foundations

This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics is physics in terms of a coherent space consisting of a line bundle over a classical phase space and an appropriate coherent product. * The kinematical structure of quantum physics and the meaning of the fundamental quantum observables are given by the symmetries of this coherent space, their infinitesimal generators, and associated operators on the quantum …