Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Field Theory of Correlated Bose-Einstein condensates: II.
  Ward-Takahashi Identities and Correlation Functions   We derive Ward-Takahashi identities for correlated Bose-Einstein condensates
based on the expressions of the first-order variations $(\delta\Psi,\delta G)$
due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc.
Jpn. $\bf 90$, 024001 (2021)] for the condensate wave function $\Psi$ and
Green's function $G$. They enable us to obtain several exact results on the
density and current correlation functions $K_{\nu\nu'}^{}$, and also express
$K_{\nu\nu'}^{}$ in terms of low-energy Green's functions and vertices. The
latter expressions open up the possibility of constructing theory of superfluid
Bose liquids in the same way as that for fermions at low temperatures. The
vertices are found to have different limits depending on which of frequency
$\omega$ and wavenumber $q$ is set equal to zero first.

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The categories of this paper are: chem-ph
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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an