[HTML][HTML] Geometry of quantum state manifolds generated by the Lie algebra operators
AR Kuzmak - Journal of Geometry and Physics, 2018 - Elsevier
Journal of Geometry and Physics, 2018•Elsevier
Abstract The Fubini–Study metric of quantum state manifold generated by the operators
which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the
manifold generated by the so (3) Lie algebra operators. Using these results, we calculate the
Fubini–Study metrics of state manifolds generated by the position and momentum operators.
Also the metrics of quantum state manifolds generated by some spin systems are obtained.
Finally, we generalize this problem for operators of an arbitrary Lie algebra.
which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the
manifold generated by the so (3) Lie algebra operators. Using these results, we calculate the
Fubini–Study metrics of state manifolds generated by the position and momentum operators.
Also the metrics of quantum state manifolds generated by some spin systems are obtained.
Finally, we generalize this problem for operators of an arbitrary Lie algebra.
Abstract
Abstract The Fubini–Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the s o (3) Lie algebra operators. Using these results, we calculate the Fubini–Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.
Elsevier