Book contents
- Quantum Worlds
- Quantum Worlds
- Copyright page
- Contents
- Contributors
- Preface
- Introduction
- Part I Ontology from Different Interpretations of Quantum Mechanics
- Part II Realism, Wave Function, and Primitive Ontology
- Part III Individuality, Distinguishability, and Locality
- Part IV Symmetries and Structure in Quantum Mechanics
- Part V The Relationship between the Quantum Ontology and the Classical World
- 17 A Closed-System Approach to Decoherence
- 18 A Logical Approach to the Quantum-to-Classical Transition
- 19 Quantum Mechanics and Molecular Structure: The Case of Optical Isomers
- Index
- References
18 - A Logical Approach to the Quantum-to-Classical Transition
from Part V - The Relationship between the Quantum Ontology and the Classical World
Published online by Cambridge University Press: 06 April 2019
Book contents
- Quantum Worlds
- Quantum Worlds
- Copyright page
- Contents
- Contributors
- Preface
- Introduction
- Part I Ontology from Different Interpretations of Quantum Mechanics
- Part II Realism, Wave Function, and Primitive Ontology
- Part III Individuality, Distinguishability, and Locality
- Part IV Symmetries and Structure in Quantum Mechanics
- Part V The Relationship between the Quantum Ontology and the Classical World
- 17 A Closed-System Approach to Decoherence
- 18 A Logical Approach to the Quantum-to-Classical Transition
- 19 Quantum Mechanics and Molecular Structure: The Case of Optical Isomers
- Index
- References
- Type
- Chapter
- Information
- Quantum WorldsPerspectives on the Ontology of Quantum Mechanics, pp. 360 - 378Publisher: Cambridge University PressPrint publication year: 2019
References
Antoine, J. P. (1969). “Dirac formalism and symmetry problems in quantum mechanics I: General Dirac formalism,” Journal of Mathematical Physics, 10: 53–69.Google Scholar
Balslev, E. and Combes, J. M. (1971). “Spectral properties of many body Schrödinger operators with dilation analytic intercations,” Communications in Mathematical Physics, 22: 280–294.Google Scholar
Birkhoff, G. and von Neumann, J. (1936). “The logic of quantum mechanics,” Annals of Mathematics, 37: 823–843.Google Scholar
Bohm, A. (1978). The Rigged Hilbert Space and Quantum Mechanics, Springer Lecture Notes in Physics. New York: Springer.Google Scholar
Bohm, A. (1993). Quantum Mechanics: Foundations and Applications. Berlin and New York: Springer.Google Scholar
Bohm, A. and Gadella, M. (1989). Dirac Kets, Gamow Vectors, and Gel’fand Triplets: The Rigged Hilbert Space Formulation of Quantum Mechanics. Berlin: Springer.CrossRefGoogle Scholar
Bub, J. (1997). Interpreting the Quantum World. Cambridge: Cambridge University Press.Google Scholar
Casati, G. and Chirikov, B. (1995a). “Comment on ‘Decoherence, chaos, and the second Law’,” Physical Review Letters, 75: 350.Google Scholar
Casati, G. and Chirikov, B. (1995b). “Quantum chaos: Unexpected complexity,” Physical Review D, 86: 220–237.Google Scholar
Casati, G., and Prosen, T. (2005). “Quantum chaos and the double-slit experiment,” Physical Review A, 72: 032111.Google Scholar
Castagnino, M. and Fortin, S. (2012). “Non-Hermitian Hamiltonians in decoherence and equilibrium theory,” Journal of Physics A, 45: 444009.Google Scholar
Castagnino, M. and Fortin, S. (2013). “Formal features of a general theoretical framework for decoherence in open and closed systems,” International Journal of Theoretical Physics, 52: 1379–1398.Google Scholar
Castagnino, M., Fortin, S., Laura, R., and Lombardi, O. (2008). “A general theoretical framework for decoherence in open and closed systems,” Classical and Quantum Gravity, 25: 154002.Google Scholar
Castagnino, M. and Gadella, M. (2006). “The problem of the classical limit of quantum mechanics and the role of self-induced decoherence,” Foundations of Physics, 36: 920–952.Google Scholar
Castagnino, M. and Lombardi, O. (2004). “Self-induced decoherence: A new approach,” Studies in History and Philosophy of Modern Physics, 35: 73–107.Google Scholar
Celeghini, E., Gadella, M., and del Olmo, M. A. (2016). “Applications of rigged Hilbert spaces in quantum mechanics and signal processing,” Journal of Mathematical Physics, 57: 072105.Google Scholar
Celeghini, E., Gadella, M., and del Olmo, M. A. (2017). “Lie algebra representations and rigged Hilbert spaces: The SO(2) case,” Acta Polytechnica, 57: 379–384.CrossRefGoogle Scholar
Celeghini, E., Gadella, M., and del Olmo, M. A. (2018). “Spherical harmonics and rigged Hilbert spaces,” Journal of Mathematical Physics, 59: 053502.Google Scholar
Civitarese, O. and Gadella, M. (2004). “Physical and mathematical aspects of Gamow states,” Physics Reports, 396: 41–113.Google Scholar
Cohen, D. (1989). An Introduction to Hilbert Space and Quantum Logic. Berlin: Springer-Verlag.Google Scholar
Dirac, P. A. M. (1933). “The Lagrangian in quantum mechanics,” Physikalische Zeitschrift der Sowjetunion, 3: 64–72.Google Scholar
Domenech, G., Holik, F., and Massri, C. (2010). “A quantum logical and geometrical approach to the study of improper mixtures,” Journal of Mathematical Physics, 51: 052108.Google Scholar
Eleuch, H. and Rotter, I. (2017). “Resonances in open quantum systems,” Physical Review A, 98: 0221117.Google Scholar
Feynman, R. P. (1942). The Principle of Least Action in Quantum Mechanics. Princeton: Princeton University. Reproduced in Feynman, R. P. and Brown, L. M. (eds.). (2005). Feynman’s Thesis: a New Approach to Quantum Theory. Singapore: World Scientific.Google Scholar
Fischer, M. C., Gutierrez-Medina, B., and Raizen, M. G. (2001). “Observation of the quantum Zeno and anti-Zeno effects in an unstable system,” Physical Review Letters, 87: 40402.Google Scholar
Fonda, L., Ghirardi, G. C., and Rimini, A. (1978). “Decay theory of unstable quantum systems,” Reports on Progress in Physics, 41: 587–631.Google Scholar
Ford, G. W. and O’Connel, R. F. (2001). “Decoherence without dissipation,” Physics Letters A, 286: 87–90.Google Scholar
Fortin, S., Holik, F., and Vanni, L. (2016). “Non-unitary evolution of quantum logics,” Springer Proceedings in Physics, 184: 219–234.Google Scholar
Fortin, S. and Vanni, L. (2014). “Quantum decoherence: A logical perspective,” Foundations of Physics, 44: 1258–1268.Google Scholar
Frasca, M. (2003). “General theorems on decoherence in the thermodynamic limit,” Physics Letters A, 308: 135–139.CrossRefGoogle Scholar
Gadella, M. and Gómez, F. (2002). “A unified mathematical formalism for the Dirac formulation of quantum mechanics,” Foundations of Physics, 32: 815–869.Google Scholar
Gadella, M. and Gómez, F. (2003). “On the mathematical basis of the Dirac formulation of quantum mechanics,” Foundations of Physics, 42: 2225–2254.Google Scholar
Gambini, R., Porto, R. A., and Pulin, J. (2007). “Fundamental decoherence from quantum gravity: A pedagogical review,” General Relativity and Gravitation, 39: 1143–1156.Google Scholar
Gambini, R. and Pulin, J. (2007). “Relational physics with real rods and clocks and the measurement problem of quantum mechanics,” Foundations of Physics, 37: 1074–1092.Google Scholar
Gambini, R. and Pulin, J. (2010). “Modern space-time and undecidability,” pp. 149–161 in Petkov, V. (ed.), Minkowski Spacetime: A Hundred Years Later. Fundamental Theories of Physics 165. Heidelberg: Springer.Google Scholar
Griffiths, R. B. (2014). “The new quantum logic,” Foundations of Physics, 44: 610–640.Google Scholar
Holik, F., Massri, C., and Ciancaglini, N. (2012). “Convex quantum logic,” International Journal of Theoretical Physics, 51: 1600–1620.Google Scholar
Holik, F., Massri, C., Plastino, A., and Zuberman, L. (2013). “On the lattice structure of probability spaces in quantum mechanics,” International Journal of Theoretical Physics, 52: 1836–1876.Google Scholar
Holik, F. and Plastino, A. (2015). “Quantum mechanics: A new turn in probability theory,” pp. 399–414 in Ezziane, Z. (ed.), Contemporary Research in Quantum Systems. New York: Nova Publishers.Google Scholar
Holik, F., Plastino, A., and Sáenz, M. (2014). “A discussion on the origin of quantum probabilities,” Annals of Physics, 340: 293–310.CrossRefGoogle Scholar
Landsman, N. P. (1993). “Deformation of algebras of observables and the classical limit of quantum mechanics,” Reviews in Mathematical Physics, 5: 775–806.Google Scholar
Losada, M., Fortin, F., Gadella, M., and Holik, F. (2018). “Dynamical algebras in quantum unstable systems,” International Journal of Modern Physics A, 33: 1850109.Google Scholar
Losada, M., Fortin, S., and Holik, F. (2018). “Classical limit and quantum logic,” International Journal of Theoretical Physics, 57: 465–475.Google Scholar
Losada, M. and Laura, R. (2014a). “Quantum histories without contrary inferences,” Annals of Physics, 351: 418–425.Google Scholar
Losada, M. and Laura, R. (2014b). “Generalized contexts and consistent histories in quantum mechanics,” Annals of Physics, 344: 263–274.Google Scholar
Losada, M., Vanni, L., and Laura, R. (2013). “Probabilities for time–dependent properties in classical and quantum mechanics,” Physical Review A, 87: 052128.Google Scholar
Losada, M., Vanni, L., and Laura, R. (2016). “The measurement process in the generalized contexts formalism for quantum histories,” International Journal of Theoretical Physics, 55: 817–824.Google Scholar
Melsheimer, O. (1974). “Rigged Hilbert space formalism as an extended mathematical formalism for quantum systems. 1. General theory,” Journal of Mathematical Physics, 15: 902–916.Google Scholar
Nakanishi, N. (1958). “A theory of clothed unstable particles,” Progress of Theoretical Physics, 19: 607–621.Google Scholar
Nielsen, M. and Chuang, I. (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.Google Scholar
Omnès, R. (1994). The Interpretation of Quantum Mechanics. Princeton: Princeton University Press.Google Scholar
Omnès, R. (2005). “Results and problems in decoherence theory,” Brazilian Journal of Physics, 35: 207–210.Google Scholar
Roberts, J. E. (1966). “Rigged Hilbert spaces in quantum mechanics,” Communications in Mathematical Physics, 3: 98–119.CrossRefGoogle Scholar
Rothe, C., Hintschich, S. L., and Monkman, A. P. (2006). “Violation of the exponential-decay law at long times,” Physical Review Letters, 96: 163601.Google Scholar
Schlosshauer, M. (2007). Decoherence and the Quantum-to-Classical Transition. Berlin: Springer.Google Scholar
von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Heidelberg: University Press.Google Scholar
Zeh, H. D. (1970). “On the interpretation of measurement in quantum theory,” Foundations of Physics, 1: 69–76.Google Scholar
Zeh, H. D. (1973). “Toward a quantum theory of observation,” Foundations of Physics, 3: 109–116.CrossRefGoogle Scholar
Zurek, W. (1982). “Environment-induced superselection rules,” Physical Review D, 26: 1862–1880.Google Scholar
Zurek, W. (1991). “Decoherence and the transition from quantum to classical,” Physics Today, 44: 36–44.Google Scholar
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