Quantum structures in Galilei general relativity
Vitolo, Raffaele
Annales de l'I.H.P. Physique théorique, Tome 71 (1999), p. 239-257 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1999-01-01
@article{AIHPA_1999__70_3_239_0,
     author = {Vitolo, Raffaele},
     title = {Quantum structures in Galilei general relativity},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {71},
     year = {1999},
     pages = {239-257},
     mrnumber = {1718181},
     zbl = {0965.81038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1999__70_3_239_0}
}

Vitolo, Raffaele. Quantum structures in Galilei general relativity. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) pp. 239-257. http://gdmltest.u-ga.fr/item/AIHPA_1999__70_3_239_0/

[1] M. Le Bellac and J.-M. Lévy-Leblond, Nuovo Cimento 14 B, 217 (1973).

[2] D. Canarutto, A. Jadczyk and M. Modugno, Quantum mechanics of a spin particle in a curved spacetime with absolute time, Rep. on Math. Phys., 36, 1 (1995), 95-140. | MR 1377229 | Zbl 0888.53052

[3] C. Duval, G. Gibbons and P. Horváthy, Phys. Rev. D, 43, 3907 (1991). | MR 1111411

[4] C. Duval, G. Burdet, H.P. Künzle and M. Perrin, Bargmann structures and Newton-Cartan theory, Phys. Rev. D, 31, n. 8 (1985), 1841-1853. | MR 787753

[5] C. Duval and H.P. Künzle, Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation, G.R.G., 16, n. 4 (1984), 333-347. | MR 741410

[6] P.L. García, The Poincaré-Cartan Invariant in the Calculus of Variations, Symposia Mathematica, 14 (1974), 219-246. | MR 406246 | Zbl 0303.53040

[7] P.L. García, Cuantificion geometrica, Memorias de la R. Acad. de Ciencias de Madrid, XI, Madrid, 1979.

[8] M. Göckeler and T. Schücker, Differential geometry, gauge theories and gravity, Cambridge Univ. Press, Cambridge, 1987. | MR 923534 | Zbl 0649.53001

[9] A. Jadczyk and M. Modugno, A scheme for Galilei general relativistic quantum mechanics, in Proceedings of the 10th Italian Conference on General Relativity and Gravitational Physics, World Scientific, New York, 1993. | Zbl 1004.83518

[10] A. Jadczyk and M. Modugno, Galilei General Relativistic Quantum Mechanics, 1993, book pre-print. | MR 1212817

[11] J. Janyška, Remarks on symplectic and contact 2-forms in relativistic theories, Boll. U.M.I., 7 (1994), 587-616. | MR 1351076 | Zbl 0857.53027

[12] J. Janyška and M. Modugno, Classical particle phase space in general relativity, Proc. "Diff. Geom. and Appl.", Brno, 1995. | MR 1406377

[13] J. Janyška and M. Modugno, Quantisable functions in general relativity, Proc. "Diff. Oper. and Math. Phys.", Coimbra; World Scientific, 1995.

[14] B. Kostant, Quantization and unitary representations, Lectures in Modern Analysis and Applications III, Springer-Verlag, 170 (1970), 87-207. | MR 294568 | Zbl 0223.53028

[15] K. Kuchař, Gravitation, geometry and nonrelativistic quantum theory, Phys. Rev. D, 22, n. 6 (1980), 1285-1299. | MR 586704

[16] H.P. Künzle, Gen. Rel. Grav. 7, 445 (1976).

[17] H.P. Künzle, General covariance and minimal gravitational coupling in Newtonian spacetime, in Geometrodynamics Proceedings (1983), edit. A. Prastaro, Tecnoprint, Bologna 1984, 37-48. | MR 823714

[18] L. Mangiarotti and M. Modugno, Fibered Spaces, Jet Spaces and Connections for Field Theories, in Proceed. of the Int. Meet. on Geometry and Physics, Pitagora Editrice, Bologna, 1983, 135-165. | MR 760841 | Zbl 0539.53026

[19] M. Modugno and R. Vitolo, Quantum connection and Poincaré-Cartan form, Atti del convegno in onore di A. Lichnerowicz, Frascati, octobre 1995; ed. G. Ferrarese, Pitagora, Bologna.

[20] E. Prugovečki, Principles of quantum general relativity, World Scientific, Singapore, 1995. | MR 1330224

[21] E. Schmutzer and J. Plebanski, Quantum mechanics in non-inertial frames of reference, Fortschritte der Physik, 25 (1977), 37-82. | MR 438967

[22] J. Sniaticki, Geometric quantization and quantum mechanics, Springer-Verlag, New York 1980. | Zbl 0429.58007

[23] J.-M. Souriau, Structures des systèmes dynamiques, Dunod, Paris 1970. | MR 260238 | Zbl 0186.58001

[24] A. Trautman, Sur la théorie Newtonienne de la gravitation, C. R. Acad. Sc. Paris, t. 257 (1963), 617-620. | MR 154718 | Zbl 0115.43105

[25] A. Trautman, Comparison of Newtonian and relativistic theories of space-time, in Perspectives in geometry and relativity (Essays in Honour of V. Hlavaty), n. 42, Indiana Univ. press, 1966, 413-425. | MR 202450

[26] W.M. Tulczyjew, An intrinsic formulation of nonrelativistic analytical mechanics and wawe mechanics, J. Geom. Phys., 2, n. 3 (1985), 93-105. | MR 851123 | Zbl 0601.70001

[27] R. Vitolo, Spherical symmetry in classical and quantum Galilei general relativity, Annales de l'Institut Henri Poincaré, 64, n. 2 (1996). | Numdam | MR 1386216 | Zbl 0854.53071

[28] R. Vitolo, Bicomplessi lagrangiani ed applicazioni alla meccanica relativistica classica e quantistica, PhD Thesis, Florence, 1996.

[29] R. Vitolo, Quantum structures in general relativistic theories, Proc. of the XII It. Conf. on G.R. and Grav. Phys., Roma, 1996, World Scientific. | MR 1609364

[30] R.O. Wells, Differential Analysis on Complex Manifolds, GTM, n. 65, Springer-Verlag, Berlin, 1980. | MR 608414 | Zbl 0435.32004

[31] N. Woodhouse, Geometric quantization, Second Ed., Clarendon Press, Oxford 1992. | MR 1183739 | Zbl 0747.58004