Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability in the higher derivative Abelian gauge field theory   We present the derivation of conserved tensors associated to higher-order
symmetries in the higher derivative Maxwell Abelian gauge field theories. In
our model, the wave operator of the higher derived theory is a $n$-th order
polynomial expressed in terms of the usual Maxwell operator. Any symmetry of
the primary wave operator gives rise to a collection of independent
higher-order symmetries of the field equations which thus leads to a series of
independent conserved quantities of derived system. In particular, by the
extension of Noether's theorem, the spacetime translation invariance of the
Maxwell primary operator results in the series of conserved second-rank tensors
which includes the standard canonical energy-momentum tensors. Although this
canonical energy is unbounded from below, by introducing a set of parameters,
the other conserved tensors in the series can be bounded which ensure the
stability of the higher derivative dynamics. In addition, with the aid of
auxiliary fields, we successfully obtain the relations between the roots
decomposition of characteristic polynomial of the wave operator and the
conserved energy-momentum tensors within the context of another equivalent
lower-order representation. Under the certain conditions, the 00-component of
the linear combination of these conserved quantities is bounded and by this
reason, the original derived theory is considered stable. Finally, as an
instructive example, we discuss the third-order derived system and analyze
extensively the stabilities in different cases of roots decomposition.

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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas