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—. A derivation of Boltzmann’s equation similar to the one presented here may be found in ref. [1]. This derivation differs from theirs in that it stays in the abstract to a later point in the derivation so that the Boltzmann collision term may be identified with the second-order term of a perturbation expansion. Also, in this derivation we are able to express the BBGY hierarchy of equations in equivalent forms by substituting either the Poisson or Moyal brackets into the equations of motion. A less detailed and complete derivation using the Green’s function method can be found inV. E. Bunakov andG. V. Matvejev:Atoms and Nuclei,332, 511 (1985). The book,Quantum Statistical Mechanics byL. Kadanoff andB. Baym (W. A. Benjamin, New York, 1962), p. 103, also contains a derivation using the Green’s function method. A summary of some of the derivations from classical mechanics can be found inR. Liboff:Introduction to the Theory of Kinetic Equations (John Wiley and Sons, New York, 1969), p. 206. A derivation of the nonrelativistic transport equation based on ref. [1] can be found inD. Long,Single Particle Kinetic Theory and Nuclear Physics, inProgress in Nuclear and Particle Physics, edited byD. Wilkinson (Pergammon Press, Oxford, 1984), p. 549.
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D. Long:Single Particle Kinetic Theory and Nuclear Physics, inProgress in Nuclear and Particle Physics, edited byD. Wilkinson (Pergammon Press, Oxford, 1984), p. 549.
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Long, D.G. The relativistic linear boltzmann transport equation applied to nucleon-nucleus and pion-nucleus transport. Riv. Nuovo Cim. 14, 1–37 (1991). https://doi.org/10.1007/BF02810068
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DOI: https://doi.org/10.1007/BF02810068