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arXiv2008

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 distance in the quantum mechanical limits.

physics.gen-ph↗

arXiv2008

Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kahler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space with the limit when Planck constant vanishes, we obtain the metric of quantum states in the configuration space without imposing this limiting condition. Here, Planck constant is absorbed in the quantity like Bohr radii. While exploring the metric structure associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr radii.

quant-ph↗