Abstract
Quantum theories with nonlinear time-evolution equations are suggested by certain continuous unitary representations of diffeomorphism groups. Their physical interpretation is discussed in the light of nonlinear gauge transformations.
In honor of Guy Rideau
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auberson, G. and Sabatier, P. C. (1994) On a Class of Homogemeous Nonlinear Schrödinger Equations, J. Math. Phys.35, 4028.
Dodonov, V. V. and Mizrahi, S. S. (1995) Uniform Nonlinear Evolution Equations for Pure and Mixed Quantum States, Annals of Physics 237, 226–268.
Doebner, H.-D. and Goldin, G. A. (1992) On a General Nonlinear Schrödinger Equation Admitting Diffusion Currents, Phys. Lett. A 162, 397–401.
Doebner, H.-D. and Goldin, G. A. (1994) Properties of Nonlinear Schrödinger Equations Associated with Diffeomorphism Group Representations, J. Phys. A: Math. Gen. 27, 1771–1780.
Doebner, H.-D., Goldin, G. A., and Nattermann, P. (1995) A Family of Nonlinear Schrödinger Equations: Linearizing Transformations, and Resulting Structure, to be published.
Feynman, R. P. and Hibbs, A. R. (1965) “Quantum Mechanics and Path Integrals”, McGraw-Hill, New York, p. 96.
Goldin, G. A. (1992) The Diffeomorphism Group Approach to Nonlinear Quantum Systems, Int. J. Mod. Phys. B 6, 1905–1916.
Goldin, G. A., Menikoff, R., and Sharp, D. H. (1981) Representations of a Local Current Algebra in Non-Simply Connected Space and the Aharonov-Bohm Effect, Journal of Mathematical Physics 22, 1664–1668.
Goldin, G. A., Menikoff, R., and Sharp, D. H. (1983) Diffeomorphism Groups, Gauge Groups, and Quantum Theory, Physical Review Letters 51, 2246–2249.
Goldin, G. A. and Sharp, D. H. (1989) Diffeomorphism Groups and Local Symmetries: Some Applications in Quantum Physics, in B. Gruber and F. Iachello, eds., “Symmetries in Science III”, Plenum, New York, 181–205.
Goldin, G. A. and Sharp, D. H. (1991) The Diffeomorphism Group Approach to Anyons, Int. J. Mod. Phys. B 5, 2625–2640.
Goldin, G. A. and Svetlichny, G. (1994) Nonlinear Schrödinger Equations and the Separation Property, J. Math. Phys. 35, 3322–3332.
Leinaas, J. M. and Myrheim, J. (1977) On the Theory of Identical Particles, Nuovo Cimento 37B, 1.
Nattermann, P. (1994) Solutions of the General Doebner-Goldin Equation via Nonlinear Transformations, in “Proceedings of the XXVI Symposium on Mathematical Physics, Torun, December 7–10, 1993”, Nicolas Copernicus University Press, Torun, 47.
Ushveridze, A. G. (1994) Dissipative Quantum Mechanics: A Special Doebner-Goldin Equation, its Properties and Exact Solutions, Phys. Lett. A 185, 123–127.
Ushveridze, A. G. (1994) The Special Doebner-Goldin Equation as a Fundamental Equation of Dissipative Quantum Mechanics, Phys. Lett. A 185, 128–132.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Goldin, G.A. (1995). Diffeomorphism Group Representations and Nonlinear Quantum Theories. In: Bertrand, J., Flato, M., Gazeau, JP., Irac-Astaud, M., Sternheimer, D. (eds) Modern Group Theoretical Methods in Physics. Mathematical Physics Studies, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8543-9_14
Download citation
DOI: https://doi.org/10.1007/978-94-015-8543-9_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4598-0
Online ISBN: 978-94-015-8543-9
eBook Packages: Springer Book Archive