Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Legendre transformations and Clairaut-type equations   It is noted that the Legendre transformations in the standard formulation of
quantum field theory have the form of functional Clairaut-type equations. It is
shown that in presence of composite fields the Clairaut-type form holds after
loop corrections are taken into account. A new solution to the functional
Clairaut-type equation appearing in field theories with composite fields is
found.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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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: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg