Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formulation of effective interaction in terms of renormalized vertices
  and propagators   One of the useful and practical methods for solving quantum-mechanical
many-body systems is to recast the full problem into a form of the effective
interaction acting within a model space of tractable size. Many of the
effective-interaction theories in nuclear physics have been formulated by use
of the so called $\hatQ$ box introduced by Kuo et.al. It has been one of the
central problems how to calculate the $\hatQ$ box accurately and efficiently.
We first show that, introducing new basis states, the Hamiltonian is
transformed to a block-tridiagonal form in terms of submatrices with small
dimension. With this transformed Hamiltonian, we next prove that the $\hatQ$
box can be expressed in two ways: One is a form of continued fraction and the
other is a simple series expansion up to second order with respect to
renormalized vertices and propagators. This procedure ensures to derive an
exact $\hatQ$ box, if the calculation converges as the dimension of the Hilbert
space tends to infinity. The $\hatQ$ box given in this study corresponds to a
non-perturbative solution for the energy-dependent effective interaction which
is often referred to as the Bloch-Horowitz or the Feshbach form. By applying
the $\hatZ$-box approach based on the $\hatQ$ box proposed previously, we
introduce a graphical method for solving the eigenvalue problem of the
Hamiltonian. The present approach has a possibility of resolving many of the
difficulties encountered in the effective-interaction theory.

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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg