35 citations · 421 across the 77 of their papers we have counts for
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Noether conservation laws in quantum mechanics
G. Sardanashvily
Being quantized, conserved Noether symmetry functions are represented by Hermitian operators in the space of solutions of the Schrodinger equation, and their mean values are conser…
Non-adiabatic holonomy operators in classical and quantum completely integrable systems
G. Giachetta, L. Mangiarotti, G. Sardanashvily
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized…
Geometric quantization of time-dependent completely integrable Hamiltonian systems
E. Fiorani, G. Giachetta, G. Sardanashvily
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. I…
Geometric quantization of mechanical systems with time-dependent parameters
G. Giachetta, L. Mangiarotti, G. Sardanashvily
Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hami…
Quantum Jacobi fields in Hamiltonian mechanics
G. Giachetta, L. Mangiarotti, G. Sardanashvily
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characteriz…
Quantum mechanics with time-dependent parameters
G. Sardanashvily
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in…