Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge parameter dependence in the background field gauge and the
  construction of an invariant charge   By using the enlarged BRS transformations we control the gauge parameter
dependence of Green functions in the background field gauge. We show that it is
unavoidable -- also if we consider the local Ward identity -- to introduce the
normalization gauge parameter $\xi_o$, which enters the Green functions of
higher orders similarly to the normalization point $\kappa$. The dependence of
Green functions on $\xi_o$ is governed by a further partial differential
equation. By modifying the Ward identity we are able to construct in 1-loop
order a gauge parameter independent combination of 2-point vector and
background vector functions. By explicit construction of the next orders we
show that this combination can be used to construct a gauge parameter
independent RG-invariant charge. However, it is seen that this RG-invariant
charge does not satisfy the differential equation of the normalization gauge
parameter $\xi_o$, and, hence, is not $\xi_o$-independent as required.

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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: cs
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: acc-phys