Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Feynman-Kac formulas for the ultra-violet renormalized Nelson model   We derive Feynman-Kac formulas for the ultra-violet renormalized Nelson
Hamiltonian with a Kato decomposable external potential and for corresponding
fiber Hamiltonians in the translation invariant case. We simultaneously treat
massive and massless bosons. Furthermore, we present a non-perturbative
construction of a renormalized Nelson Hamiltonian in the non-Fock
representation defined as the generator of a corresponding Feynman-Kac
semi-group. Our novel analysis of the vacuum expectation of the Feynman-Kac
integrands shows that, if the external potential and the Pauli-principle are
dropped, then the spectrum of the $N$-particle renormalized Nelson Hamiltonian
is bounded from below by some negative universal constant times $g^4N^3$, for
all values of the coupling constant $g$. A variational argument also yields an
upper bound of the same form for large $g^2N$. We further verify that the
semi-groups generated by the ultra-violet renormalized Nelson Hamiltonian and
its non-Fock version are positivity improving with respect to a natural
self-dual cone, if the Pauli principle is ignored. In another application we
discuss continuity properties of elements in the range of the semi-group of the
renormalized Nelson Hamiltonian.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin