Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An operator representation for Matsubara sums   In the context of the imaginary-time formalism for a scalar thermal field
theory, it is shown that the result of performing the sums over Matsubara
frequencies associated with loop Feynman diagrams can be written, for some
classes of diagrams, in terms of the action of a simple linear operator on the
corresponding energy integrals of the Euclidean theory at T=0. In its simplest
form the referred operator depends only on the number of internal propagators
of the graph.
  More precisely, it is shown explicitly that this \emph{thermal operator
representation} holds for two generic classes of diagrams, namely, the
two-vertex diagram with an arbitrary number of internal propagators, and the
one-loop diagram with an arbitrary number of vertices.
  The validity of the thermal operator representation for diagrams of more
complicated topologies remains an open problem. Its correctness is shown to be
equivalent to the correctness of some diagrammatic rules proposed a few years
ago.

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The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an