caa a22 4500 463196031 CHVBK 20180406164923.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10773-007-9438-7 doi (NATIONALLICENCE)springer-10.1007/s10773-007-9438-7 Aalok, Department of Physics, University of Rajasthan, 302004, Jaipur, India aut Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective [Elektronische Daten] [Aalok,] This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler 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 when the limit ℏ→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ℏ→0. Here Planck's constant ℏ is absorbed in the quantity like Bohr radii $\frac{1}{2mZ\alpha}\sim a_{0}$ . While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr's radii as: ds 2=a 0 2 (∇ Ψ)2. Springer Science+Business Media, LLC, 2007 Quantum state space nationallicence Projective Hilbert space nationallicence Manifold nationallicence Pseudo-Riemannian manifold nationallicence Local gauge transformations nationallicence Invariance nationallicence Connections nationallicence Projections nationallicence Fiber bundle nationallicence Symmetries nationallicence International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/12(2007-12-01), 3216-3229 0020-7748 46:12<3216 2007 46 10773 https://doi.org/10.1007/s10773-007-9438-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9438-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Aalok Department of Physics, University of Rajasthan, 302004, Jaipur, India aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/12(2007-12-01), 3216-3229 0020-7748 46:12<3216 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer