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We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory.
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The machinary of mode coupling theory is discussed in W. Goetze, in Liquids, Freezing, and the Glass Transitions, ed. by J. P. Hansen, D. Levesque and J. Zinn-Justin, S. P. Das, Statistical Physics of iquids at Freezing and Beyond, (Cambridge U. press, 2011). From our perspective see P. Spyridis and G. Mazenko, unpublished
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If G ρ ρ G_{\rho\rho} is the density autocorrelation function, and we define the limit lim t → ∞ G ρ ρ ( q , t ) = F ( q ) \lim_{t\rightarrow\infty}G_{\rho\rho}(q,t)=F(q) (222)
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For some background on Smolukowski dynamics, see ref. 20 in FTSPD
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The actual definitions of the variables B B are different in the two cases SD and ND
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The fluctuation dissipation theorem gives relationships between cumulants with response fields and those without. We refer to a fluctuation-dissipation symmetry (FDS) to characterize the transformation which leaves the action A A invariant. See SDENE for the SD case
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