Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Foundation of the Relativistic Dynamics with the Tachyon   The theoretical foundation of the object moving faster than light in vacuum
({\it tachyon}) is still missing or incomplete. Here we present the classical
foundation of the relativistic dynamics including the tachyon. An anomalous
sign-factor extracted from the transformation of ${ \sqrt{1-u^{2}/c^{2} } }$
under the Lorentz transformation, which has been always missed in the usual
formulation of the tachyon, has a crucial role in the dynamics of the tachyon.
Due to this factor the mass of the tachyon transforms in the unusual way
although the energy and momentum, which are defined as the conserved quantities
in all uniformly moving systems, transform in the usual way as in the case of
the object moving slower than light ({\it bradyon}). We show that this result
can be also obtained from the least action approach. On the other hand, we show
that the ambiguities for the description of the dynamics for the object moving
with the velocity of light ({\it luxon}) can be consistently removed only by
introducing a new dynamical variable. Furthermore, by using the fundamental
definition of the momentum and energy we show that the zero-point energy for
any kind of the objects, {\it i.e.}, the tachyon, bradyon, and luxon, which has
been known as the undetermined constant, should satisfy some constraints for
consistency, and we note that this is essentially another novel relativistic
effect. Finally, we remark about the several unsolved problems.

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The categories of this paper are: plasm-ph
2
The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom