Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

Historical Background as an Essential Ingredient for the Understanding of New Developments in Quantum Mechanics

Paper is taken out with immediate effect.

物理空间的曲率与几何投影：量子力学与相对论的一种可能几何理解

Curvature of Physical Space and Geometric Projection: A Possible Geometric Understanding of Quantum Mechanics and Relativity

本文对比薛定谔方程与雅可比场方程，提出微观物理空间截面曲率表达式，尝试为量子力学与相对论提供统一几何理解，并拓展至统计力学。

Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems

This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. Basic geometric and physical properties of the canonical nonholonomic deformations of G. Perelman entropy functionals and geometric flows evolution equations of classical mechanical systems are described. There are studied projections of such F- and W-functionals on Lorentz spacetime manifolds and three-dimensional spacelike hypersurfaces. These functionals are used for elaborating relativistic thermodynamic models for Lagrange--Hamilton…

局部量子力学对singlet态的预测使用几何代数

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

本文通过几何代数方法，利用局部测量函数推导了singlet态的量子力学预测，并通过计算模拟验证了结果。

Background Independent Quantum Mechanics, Gravity, and Physics at Short Distance: Some Insights

In the present discussion Background Independent framework of Quantum Mechanics and its possible implications in the studies of gravity and Physics at short distance are addressed. The expression of the metric of quantum state space $g_{μν}$ which is intrinsically a quantized quantity, is identified in terms of Compton wavelength as: $[<\partial_μψ\mid\partial_νψ> - <\partial_μψ\midψ> <ψ\mid\partial_νψ>] = 1 / \lambdabar_C^2 (=m_0^2c^2 / \hbar^2})$. The discussion also sheds light on the notion of neighborhood in quantum evolution, and various constraints on the possibilities of smallness of d…