Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental dynamical equations for spinor wave functions. I.
  Levy-Leblond and Schrodinger equations   A search for fundamental (Galilean invariant) dynamical equations for two and
four-component spinor wave functions is conducted in Galilean space-time. A
dynamical equation is considered as fundamental if it is invariant under the
symmetry operators of the group of the Galilei metric and if its state
functions transform like the irreducible representations of the group of the
metric. It is shown that there are no Galilean invariant equations for
two-component spinor wave functions. A method to derive the L\'evy-Leblond
equation for a four-component spinor wave function is presented. It is formally
proved that the L\'evy-Leblond and Schr\"odinger equations are the only
Galilean invariant four-component spinor equations that can be obtained with
the Schr\"odinger phase factor. Physical implications of the obtained results
and their relationships to the Pauli-Schr\"odinger equation are discussed.

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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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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: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn