Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ghost Problems from Pauli-Villars to Fourth-Order Quantum Gravity and
  their Resolution   We review the history of the ghost problem in quantum field theory from the
Pauli-Villars regulator theory to currently popular fourth-order derivative
quantum gravity theories. While these theories all appear to have
unitarity-violating ghost states with negative norm, we show that in fact these
ghost states only appear because the theories are being formulated in the wrong
Hilbert space. In these theories the Hamiltonians are not Hermitian but instead
possess an antilinear symmetry. Consequently, one cannot use inner products
that are built out of states and their Hermitian conjugates. Rather, one must
use inner products built out of states and their conjugates with respect to the
antilinear symmetry, and these latter inner products are positive. In this way
one can build quantum theories of gravity in four spacetime dimensions that are
unitary.

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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
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg