My Library: Time-Dependent Mechanics

Classical and quantum non-autonomous mechanics with respect to different reference frames is formulated in terms of fibre bundles over the time axis R.

The file Library2.pdf (7 Mb) contains the attached PDF files of my main works in classical and quantum time-dependent (non-autonomous) mechanics.

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric and Algebraic Topological Methods in Quantum Mechanics (World Scientific, Singapore, 2005)

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (World Scientific, Singapore, 2010)

G.Sardanashvily, Hamilton time-dependent mechanics, J. Math. Phys. 39 (1998) 2714-2729

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Non-holonomic constraints in time-dependent mechanics, J. Math. Phys. 40 (1999) 1376-1390

L.Mangiarotti and G.Sardanashvily, On the geodesic form of second order dynamic equations, J. Math. Phys. 41 (2000) 835-844

L.Mangiarotti and G.Sardanashvily, Constraints in Hamiltonian time-dependent mechanics,

J. Math. Phys. 41 (2000) 2858-2876

G.Sardanashvily, Classical and quantum mechanics with time-dependent parameters, J. Math. Phys. 41 (2000) 5245-5255

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Covariant geometric quantization of nonrelativistic time-dependent mechanics, J. Math. Phys. 43 (2002) 56-68

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric quantization of mechanical systems with time-dependent parameters, J. Math. Phys. 43 (2002) 2882-2894

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric quantization of completely integrable Hamiltonian systems in action-angle coordinates, Phys. Lett. A 301 (2002) 53-57

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Action-angle coordinates for time-dependent completely integrable Hamiltonian systems, J. Phys. A 35 (2002) L439-L445

E.Fiorani, G.Giachetta and G.Sardanashvily, Geometric quantization of time-dependent completely integrable Hamiltonian systems, J. Math. Phys. 43 (2002) 5013-5025

E.Fiorani, G.Giachetta and G.Sardanashvily, The Liouville -- Arnold -- Nekhoroshev theorem for non-compact invariant manifolds, J. Phys. A 36 (2003) L101-L107

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Jacobi fields of completely integrable systems, Phys. Lett. A 309 (2003) 382-386

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Bi-Hamiltonian partially integrable systems, J. Math. Phys. 44 (2003) 1984-1987

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Nonadiabatic holonomy operators in classical and quantum completely integrable systems, J. Math. Phys. 45 (2004) 76-86

E.Fiorani and G.Sardanashvily, Noncommutative integrability on noncompact invariant manifolds, J. Phys. A 39 (2006) 14035-14042

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Quantization of noncommutative completely integrable systems, Phys. Lett. A 362 (2007) 138-142

E.Fiorani and G.Sardanashvily, Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds, J. Math. Phys. 48 (2007) 032901

L.Mangiarotti and G.Sardanashvily, Quantum mechanics with respect to different reference frames, J. Math. Phys. 48 (2007) 082104

G.Sardanashvily, Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system, Int. J. Geom. Methods Mod. Phys. 6 (2009) 1391-1420

G.Sardanashvily, Relativistic mechanics in a general setting, Int. J. Geom. Methods Mod. Phys. 7 (2010) 1307-1319