Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Poisson structure of the mean-field equations in the Phi^4 theory   We show that the mean-field time dependent equations in the Phi^4 theory can
be put into a classical non-canonical hamiltonian framework with a Poisson
structure which is a generalization of the standard Poisson bracket. The
Heisenberg invariant appears as a structural invariant of the Poisson tensor.
(To be pubished in Annals of Physics)

28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int