Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifestly Finite Perturbation Theory for the Short-Distance Expansion
  of Correlation Functions in the Two Dimensional Ising Model   In the spirit of classic works of Wilson on the renormalization group and
operator product expansion, a new framework for the study of the theory space
of euclidean quantum field theories has been introduced. This formalism is
particularly useful for elucidating the structure of the short-distance
expansions of the $n$-point functions of a renormalizable quantum field theory
near a non-trivial fixed point. We review and apply this formalism in the study
of the scaling limit of the two dimensional massive Ising model.
Renormalization group analysis and operator product expansions determine all
the non-analytic mass dependence of the short-distance expansion of the
correlation functions. An extension of the first order variational formula to
higher orders provides a manifestly finite scheme for the perturbative
calculation of the operator product coefficients to any order in parameters. A
perturbative expansion of the correlation functions follows. We implement this
scheme for a systematic study of correlation functions involving two spin
operators. We show how the necessary non-trivial integrals can be calculated.
As two concrete examples we explicitly calculate the short-distance expansion
of the spin-spin correlation function to third order and the spin-spin-energy
density correlation function to first order in the mass. We also discuss the
applicability of our results to perturbations near other non-trivial fixed
points corresponding to other unitary minimal models.

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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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: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat