Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge
  Schwinger Model II   Canonical methods are not sufficient to properly quantize space-like axial
gauges. In this paper, we obtain guiding principles which allow the
construction of an extended Hamiltonian formalism for pure space-like axial
gauge fields. To do so, we clarify the general role residual gauge fields play
in the space-like axial gauge Schwinger model. In all the calculations we fix
the gauge using a rule, $n{\cdot}A=0$, where $n$ is a space-like constant
vector and we refer to its direction as $x_-$. Then, to begin with, we
construct a formulation in which the quantization surface is space-like but not
parallel to the direction of $n$. The quantization surface has a parameter
which allows us to rotate it, but when we do so we keep the direction of the
gauge field fixed. In that formulation we can use canonical methods. We
bosonize the model to simplify the investigation. We find that the
antiderivative, $({\partial}_-)^{-1}$, is ill-defined whatever quantization
coordinates we use as long as the direction of $n$ is space-like. We find that
the physical part of the dipole ghost field includes infrared divergences.
However, we also find that if we introduce residual gauge fields in such a way
that the dipole ghost field satisfies the canonical commutation relations, then
the residual gauge fields are determined so as to regularize the infrared
divergences contained in the physical part. The propagators then take the form
prescribed by Mandelstam and Leibbrandt. We make use of these properties to
develop guiding principles which allow us to construct consistent operator
solutions in the pure space-like case where the quantization surface is
parallel to the direction of $n$ and canonical methods do not suffice.

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The categories of this paper are: q-bio
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The categories of this paper are: cs
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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: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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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: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: bayes-an