Keywords
- Wiener Process
- Schrodinger Equation
- Springer Lecture Note
- Stochastic Mechanic
- Markov Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ph. Blanchard, Ph. Combe, and W. Zheng, “Mathematical and Physical Aspects of Stochastic Mechanics,” Springer Lecture Notes in Phys. 281, 1987.
R. Bowling Barnes and S. Silverman, “Brownian motion as a natural limit to all measuring processes,” Rev. Mod. Phys. 6 (1934), 162–192.
Eric A. Carlen, “Conservative diffusions,” Commun. Math. Phys. 94 (1984), 293–315.
—, “Potential scattering in stochastic mechanics,” Ann. Inst. H. Poincaré 42 (1985), 407–428.
—, “The pathwise description of quantum scattering in stochastic mechanics,” in Stochastic Processes in Classical and Quantum Systems, Proc., Ascona, Switzerland 1985, ed. S. Albeverio, G. Casati, and D. Merlini, Springer Lecture Notes in Phys. 262 (1986), 139–147.
E. A. Carlen and A. Truman, “Sojourn times and first hitting times in stochastic mechanics,” in Fundamental Aspects of Quantum Theory, ed. Vittorio Gorini and Alberto Frigerio, Plenum, New York (1986), 151–161.
Bryce S. DeWitt, “Dynamical theory in curved spaces I. A review of the classical and quantum action principles,” Rev. Mod. Phys. 29 (1957), 377–397.
Thaddeus George Dankel, Jr., “Mechanics on manifolds and the incorporation of spin into Nelson's stochastic mechanics,” Arch. Rational Mech. Anal. 37 (1970), 192–222.
D. Dohrn and F. Guerra, “Nelson's stochastic mechanics on Riemannian manifolds,” Lettere al Nuovo Cimento 22 (1978), 121–127.
—, “Geodesic correction to stochastic parallel displacement of tensors,” in Stochastic Behavior in Classical and Quantum Physics, ed. G. Casati and J. Ford, Springer Lecture Notes in Phys. 93 (1979), 241–249.
Ian Davies and Aubrey Truman, eds., Proceedings of a conference held in Swansea 1986, to appear in Springer Lecture Notes in Math.
Imre Fényes, “Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik,” Zeitschrift für Phys. 132 (1952), 81–106.
Richard P. Feynman, “QED—The Strange Theory of Light and Matter,” Princeton University Press, Princeton, NJ, 1985.
Francesco Guerra, “Carlen processes: a new class of diffusions with singular drifts,” in Quantum Probability and Applications II, Proc. Workshop Heidelberg 1984, ed. L. Accardi and W. von Waldenfels, Springer Lecture Notes in Math. 1136 (1985), 259–267.
James Glimm and Arthur Jaffe, “Quantum Physics—A Functional Integral Point of View,” Springer-Verlag, New York, 1981.
Francesco Guerra and Maria I. Loffredo, “Thermal mixtures in stochastic mechanics,” Lettere al Nuovo Cimento 30 (1981), 81–87.
Francesco Guerra and Laura M. Morato, “Quantization of dynamical systems and stochastic control theory,” Phys. Rev. D 27 (1983), 1774–1786.
Francesco Guerra and Patrizia Ruggiero, “A new interpretation of the Euclidean-Markov field in the framework of physical Minkowski space-time,” Phys. Rev. Letters 31 (1973), 1022–1025.
Kiyosi Itô, “The Brownian motion and tensor fields on a Riemannian manifold,” Proc. Int. Congress Math. (Stockholm) (1962), 536–539.
John D. Lafferty, “The density manifold and configuration space quantization,” to appear in Trans. Am. Math. Soc.
Michael G. G. Laidlaw and Cécile Morette DeWitt, “Feynman functional integrals for systems of indistinguishable particles,” Phys. Rev. D 3 (1971), 1375–1378.
N. D. Mermin, “Bringing home the quantum world: quantum mysteries for anybody,” Am. J. Phys. 49 (1981), 940–943.
Edward Nelson, “Quantum fluctuations—an introduction,” in Mathematical Physics VII, Proc. VIIth Int. Congress on Math. Phys., Boulder, CO, 1983, ed. W. E. Brittin, K. E. Gustafson, and W. Wyss, North-Holland, Amsterdam, (1984), 509–519.
—, “Quantum Fluctuations,” Princeton University Press, Princeton, NJ, 1985.
—, “Critical diffusions,” in Séminaire de Probabilités XIX 1983/84, ed. J. Azéma and M. Yor, Springer Lecture Notes in Math. 1123 (1985), 1–11.
—, “Field theory and the future of stochastic mechanics,” in stochastic Processes in Classical and Quantum Systems, Proc., Ascona, Switzerland 1985, ed. S. Albeverio, G. Casati, and D. Merlini, Springer Lecture Notes in Phys. 262 (1986), 438–469.
—, “The locality problem in stochastic mechanics,” in New Techniques and Ideas in Quantum Measurement Theory, ed. Daniel M. Greenberger, Ann. N. Y. Acad. Sci. 480 (1986), 533–538.
L. Pitt, “A Markov property for Gaussian processes with a multidimensional parameter,” Arch. Rational Mech. Anal. 43 (1971), 367–391.
Lawrence Schulman, “A path integral for spin,” Phys. Rev. 176 (1968), 1558–1569.
Barry Simon, “The P(Φ)2 Euclidean (Quantum) Field Theory,” Princeton University Press, Princeton, NJ, 1974.
D. S. Shucker, “Stochastic mechanics of systems with zero potential,” J. Functional Anal. 38 (1980), 146–155.
Timothy C. Wallstrom, Thesis, Princeton University, to appear.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Nelson, E. (1988). Stochastic mechanics and random fields. In: Hennequin, PL. (eds) École d'Été de Probabilités de Saint-Flour XV–XVII, 1985–87. Lecture Notes in Mathematics, vol 1362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086184
Download citation
DOI: https://doi.org/10.1007/BFb0086184
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50549-5
Online ISBN: 978-3-540-46042-8
eBook Packages: Springer Book Archive
