Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic transformations of a beam matrix with real Pauli and Dirac
  matrices   A basic problem in linear particle optics is to find a symplectic
transformation that brings the (symmetric) beam matrix to a special diagonal
form, called normal form. The conventional way to do this involves an
eigenvalue-decomposition of a matrix related to the beam matrix, and may be
applied to the case of 1, 2 or 3 particle degrees of freedom. For 2 degrees of
freedom, a different normalization method involving "real Dirac matrices" has
recently been proposed. In the present article, the mathematics of real Dirac
matrices is presented differently. Another normalization recipe is given, and
more general decoupling problems are solved. A 3D visual representation of the
beam matrix is provided. The corresponding normalization method for 1 degree of
freedom involving "real Pauli matrices" is also given.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ