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In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states.
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1927
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1932
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H.J. Groenewold, “On the principles of elementary quantum mechanics,” Physica 12
1946
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J. E. Moyal, “Quantum mechanics as a statistical theory,” Proc. Cambridge Phil. Soc. 45
1949
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L. Van Hove, “Sur certaines representations unitaires d’un groupe infini de transformations,” Mem. Acad. Roy. Belg. 26
1951
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1976
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1976
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E. Gozzi, M. Reuter, and W. D. Thacker, “Hidden BRS Invariance in Classical Mechanics 2,” Phys. Rev. D40
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1990
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E. Gozzi and M. Reuter, “Algebraic Characterization of Ergodicity,” Phys. Lett. B233
1990
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N.L. Balazs and A. Voros, “Wigner’s function and tunneling,” Annals of Phys. 199
1990
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M.S. Marinov, “A new type of phase-space path integral,” Physics Letters A 153
1991
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E. Gozzi and M. Reuter, “Quantum deformed geometry on phase space,” Mod. Phys. Lett. A8
1993
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B. Felsager, Geometry, Particles and Fields (Springer-Verlag, New York, 1998)
1998
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C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, New York, 1999)
1999
A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University Press, New York, 2011)
2011
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E. Gozzi and R. Penco, “Three Approaches to Classical Thermal Field Theory,” Annals Phys. 326
2011
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2011
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2014
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E. Gozzi and D. Mauro, “A New look at the Schouten-Nijenhuis, Frolicher-Nijenhuis and Nijenhuis-Richardson brackets for symplectic spaces,” J. Math. Phys. 41
2000
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M. Chaichian and A. Demichev, Path integrals in physics. Vol. 1: Stochastic processes and quantum mechanics (CRC Press, Boca Raton, 2001)
2001
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E. Deotto and E. Gozzi, “On the ’universal’ N=2 supersymmetry of classical mechanics,” Int. J. Mod. Phys. A16
2001
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M. Razavy, Quantum Theory of Tunneling (World Scientific, Singapore, 2003)
2003
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O. Vallée and M. Soares, Airy Functions and Applications to Physics (World Scientific, Singapore, 2004)
2004
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A. A. Abrikosov, Jr., E. Gozzi, and D. Mauro, “Geometric dequantization,” Annals Phys. 317
2005
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2014
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U. C. Täuber, Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge University Press, New York, 2014)
2014
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2015
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2016
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E. Gozzi, E. Cattaruzza, and C. Pagani, Path Integrals for Pedestrians (World Scientific, Singapore, 2016)
2016
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2017
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Job Feldbrugge, Jean-Luc Lehners, and Neil Turok, “Lorentzian Quantum Cosmology,” Phys. Rev. D95
2017
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C. Pagani, “Note on the super-extended Moyal formalism and its BBGKY hierarchy,” Annals Phys. 385
2017
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M. Crossley, P. Glorioso, and H. Liu, “Effective field theory of dissipative fluids,” JHEP 09
2017
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2017
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W. Dittrich and M. Reuter, Classical and Quantum Dynamics (Springer, New York, 2020)
2020
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