Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities
  and Renormalization   The renormalization properties of two local gauge invariant composite
operators $(O,R^a_{\mu})$ corresponding, respectively, to the gauge invariant
description of the Higgs particle and of the massive gauge vector boson, are
analyzed to all orders in perturbation theory by means of the algebraic
renormalization in the $SU(2)$ Higgs model, with a single scalar in the
fundamental representation, when quantized in the Landau gauge in Euclidean
space-time. The present analysis generalizes earlier results presented in the
case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an
exact custodial symmetry, is derived for the first time, with deep consequences
at the quantum level. In particular, the gauge invariant vector operators
$R^a_{\mu}$ turn out to be the conserved Noether currents of the
above-mentioned custodial symmetry. As such, these composite operators do not
renormalize, as expressed by the fact that the renormalization $Z$-factors of
the corresponding external sources, needed to define the operators $R^a_{\mu}$
at the quantum level, do not receive any quantum corrections. Another
consistency feature of our analysis is that the longitudinal component of the
two-point correlation function $\langle R^a_\mu(p) R^b_\nu(-p) \rangle$
exhibits only a tree level non-vanishing contribution which, moreover, is
momentum independent, being thus not associated to any physical propagating
mode. Finally, we point out that the renowned non-renormalization theorem for
the ghost-antighost-vector boson vertex in Landau gauge remains true to all
orders, also in presence of the Higgs field.

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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc