Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonequilibrium Evolution of Correlation Functions: A Canonical Approach   We study nonequilibrium evolution in a self-interacting quantum field theory
invariant under space translation only by using a canonical approach based on
the recently developed Liouville-von Neumann formalism. The method is first
used to obtain the correlation functions both in and beyond the Hartree
approximation, for the quantum mechanical analog of the $\phi^{4}$ model. The
technique involves representing the Hamiltonian in a Fock basis of annihilation
and creation operators. By separating it into a solvable Gaussian part
involving quadratic terms and a perturbation of quartic terms, it is possible
to find the improved vacuum state to any desired order. The correlation
functions for the field theory are then investigated in the Hartree
approximation and those beyond the Hartree approximation are obtained by
finding the improved vacuum state corrected up to ${\cal O}(\lambda^2)$. These
correlation functions take into account next-to-leading and
next-to-next-to-leading order effects in the coupling constant. We also use the
Heisenberg formalism to obtain the time evolution equations for the equal-time,
connected correlation functions beyond the leading order. These equations are
derived by including the connected 4-point functions in the hierarchy. The
resulting coupled set of equations form a part of infinite hierarchy of coupled
equations relating the various connected n-point functions. The connection with
other approaches based on the path integral formalism is established and the
physical implications of the set of equations are discussed with particular
emphasis on thermalization.

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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: math-ph