Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Expansion Term In Hamilton's Equations   For any given spacetime the choice of time coordinate is undetermined. A
particular choice is the absolute time associated with a preferred vector
field. Using the absolute time Hamilton's equations are
  $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,
  $+ (\delta H_{c})/(\delta \pi)=\dot{q}$,
  where $\Theta = V^{a}_{.;a}$ is the expansion of the vector field. Thus there
is a hitherto unnoticed term in the expansion of the preferred vector field.
Hamilton's equations can be used to describe fluid motion. In this case the
absolute time is the time associated with the fluid's co-moving vector. As
measured by this absolute time the expansion term is present. Similarly in
cosmology, each observer has a co-moving vector and Hamilton's equations again
have an expansion term. It is necessary to include the expansion term to
quantize systems such as the above by the canonical method of replacing Dirac
brackets by commutators. Hamilton's equations in this form do not have a
corresponding sympletic form. Replacing the expansion by a particle number
$N\equiv exp(-\int\Theta d \ta)$ and introducing the particle numbers conjugate
momentum $\pi^{N}$ the standard sympletic form can be recovered with two extra
fields N and $\pi^N$. Briefly the possibility of a non-standard sympletic form
and the further possibility of there being a non-zero Finsler curvature
corresponding to this are looked at.

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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin