Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac Representation of Dynamically-Generated Elementary-Particle Mass   Special-relativistic dynamically-generated elementary-particle mass is
represented by a self-adjoint energy operator acting on a rigged Hilbert space
(RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy
operator is not the generator of infinitesimal wave-function evolution in
classical time. Ray evolution is generated by action-carrying Feynman paths.
Extending quantum-theoretic formalism which Dirac invented and applied
non-relativistically, unitary Poincar\'e -group representation is provided by
the wave functions of a spacelike entity that we call 'preon'. Although the
term 'preon observable' is misleading, six continuous Feynman-path-contacting
preon coordinates specify spatial location (3 coordinates),
lightlike-velocity-direction (2 coordinates) and transverse polarization (1
coordinate). Velocity and spatial location combine to define a preon time
operator conjugate to the energy operator. In RHS bases alternative to
functions over the group manifold, the wave function depends on a preon
'velocity-helicity' integer or half-odd integer) and a positive-lightlike
velocity 4-vector that is Lorentz-orthogonal to a canonically-conjugate pair of
spacelike 4-vectors. One 4-vector prescribes location in preon spacetime while
its conjugate prescribes preon energy-momentum. Emulating the
Schr\"odinger-dubbed 'zitterbewegung' of Dirac's 'relativistic' electron, mass
for any spinning (positive-timelike) elementary particle accompanies a
reflection-symmetric fluctuation of preon lightlike velocity and
velocity-helicity. But (departing from Dirac), a tiny elementary-particle
'longitudinal' spatial extension accompanies a huge fluctuation of preon
longitudinal momentum dictated by motionless-particle reflection symmetry about
the plane perpendicular to spin direction.

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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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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: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn