Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A robust generalization of the Legendre transform for QFT   Although perturbative quantum field theory is highly successful, it possesses
a number of well-known analytic problems, from ultraviolet and infrared
divergencies to the divergence of the perturbative expansion itself. As a
consequence, it has been difficult, for example, to prove with full rigor that
the Legendre transform of the quantum effective action is the generating
functional of connected graphs. Here, we give a rigorous proof of this central
fact. To this end, we show that the Legendre transform can be re-defined purely
combinatorially and that it ultimately reduces to a simple homological
relation, the Euler characteristic for tree graphs. This result suggests that,
similarly, also the quantum field theoretic path integral, being a Fourier
transform, may be reducible to an underlying purely algebraic structure.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga