78
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Stochastic quantization of finite dimensional systems with electromagnetic interactions

&
Pages 295-306 | Received 31 Mar 2010, Accepted 30 Jul 2010, Published online: 30 Mar 2011

References

  • Aldrovandi , E. , Dohrn , D. and Guerra , F. 1992 . The Lagrangian approach to stochastic variational principles on curved manifolds . Acta Applicandae Math. , 26 : 219 – 236 .
  • Caliari , M. , Inverso , G. and Morato , L.M. 2005 . Dissipation caused by a vorticity field and formation of singularities in Madelung fluid . New J. Phys. , 6 : 69
  • Caliari , M. , Loffredo , M.I. , Morato , L.M. and Zuccher , S. 2008 . Cubic nonlinear Schroedinger equation with vorticity . New J. Phys. , 10 : 123020
  • Carlen , E. 1984 . Conservative diffusions . Commun. Math. Phys. , 94 : 293
  • Faris , W.G. 2006 . Diffusion, Quantum Theory and Radically Elementary Mathematics , Princeton : Princeton University Press .
  • Föllmer , H. 1986 . “ Time reversal on Wiener space ” . In Stochastic Process in Mathematics and Physics , Lecture Notes in Mathematics Vol. 1158 , 119 – 129 . New York : Springer .
  • Föllmer , H. and Wakolbinger , A. 1986 . Time reversal of infinite dimensional diffusions . Stoch. Process. Appl. , 22 : 56 – 77 .
  • Guerra , F. and Morato , L. 1983 . Quantization of dynamical systems and stochastic control theory . Phys. Rev. D , 27 : 1774 – 1786 .
  • Lin , C.C. 1963 . “ Hydrodynamics of helium II ” . In Liquid Helium , 93 – 146 . New York : MacMillan . Proceedings of the International School of Physics, Course XXI
  • Loffredo , M.I. and Morato , L.M. 1989 . Lagrangian variational principle in Stochastic Mechanics: Gauge structure and stability . J. Math. Phys. , 30 : 354 – 360 .
  • Loffredo , M.I. and Morato , L.M. 2007 . Stochastic quantization for a system of N identical interacting Bose particles . J. Phys. A: Math. Theor. , 40 : 870
  • Loffredo , M. and Ugolini , S. 1996 . Eulerian versus Lagrangian variational principles in stochastic mechanics . Meccanica , 31 : 195
  • Morato , L.M. 1985 . Path-wise calculus of variations with the classical action and quantum systems . Phys. Rev. D , 31 : 1982
  • Morato , L.M. and Ugolini , S. 1994 . Gaussian solutions to the Lagrangian variational problem in Stochastic Mechanics . Annales de l'IHP , 60 : 322
  • Morato , L.M. and Ugolini , S. 1994 . A connection between quantum dynamics and approximation of Markov diffusions . J. Math. Phys. , 9 : 4505
  • Nelson , E. 1985 . Quantum Fluctuations , Princeton : Princeton University Press .
  • Parisi , G. and Wu , Y. 1981 . Perturbation theory without gauge fixing . Sci. Sin. , 24 : 484
  • Posilicano , A. and Ugolini , S. 1993 . Convergence of Nelson diffusions with time-dependent electromagnetic potentials . J. Math. Phys. , 34 ( 11 ) : 5028 – 5036 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.