6. Aalok Pandya, Ashok K. Nagawat, The Metric of Quantum States Revisited

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Volume 19: Pages 263-268, 2006

The Metric of Quantum States Revisited

Aalok Pandya 1,2, Ashok K. Nagawat 3

1Department of Physics, University of Rajasthan, Jaipur 302004, India

2Jaipur Engineering College and Research Centre (JECRC), Jaipur, India

3Department of Physics, University of Rajasthan, Jaipur 302004, India

A generalized definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan is reproduced and verified here by this generalized definition. The metric of quantum states in the configuration space and its possible geometrical framework are explored. Also, invariance of the metric of quantum states under local gauge transformations, coordinate transformations, and the relativistic transformations is discussed.

Keywords: quantum state space, projective Hilbert space, manifold, pseudoRiemannian manifold, local gauge transformations, invariance, connections, projections, fiber bundle, symmetries

Received: June 3, 2005; Published online: December 15, 2008