  One of the most important problem in hadron physics is to establish the
Lorentz-invariant classification scheme of composite hadrons, extending the
framework of non-relativistic quark model. We present an attempt, by developing
proper-time $\tau$ quantum mechanics on a multi-quark system in particle frame
(with constant boost velocity $\boldsymbol{v}$). We start from the variational
method on a classical mechanics action where a constituent quark has Pauli-type
$SU(2)_{\sigma}$ spin. Then the $SU(2)_{\mathfrak{m}}$ symmetry, concerning the
sign-reversal on quark mass, has arisen with the basic vectors, the normal
Dirac spinor with $J^{P}=(1/2)^{+}$ and the chiral one with $J^{P}=(1/2)^{-}$,
appearing as a "shadow" of the former. Herewith, the mass reversal between
these basic vectors become equivalent to the chirality, which is a symmetry of
the standard gauge theory. We describe the role of chirality in hadron
spectroscopy and regard it as attribute {$\chi$} of "elementary" hadrons in
addition to {$J, P, C$}. A novel feature of our hadron spectroscopy is, in the
example of $q\bar{q}$ meson system, that the "Regge trajectories", are given by
mass-squared vs. the number of quantum $N$ ; where $M^2 =M_{0}^2 +2N\Omega$
($N=2n$, $n$ the radial quantum number, $\Omega$ the oscillator quantum), and
the intrinsic spin of hadrons $\boldsymbol{J}$ comes only from quark spin
$\boldsymbol{S}$, $\boldsymbol{J}=\boldsymbol{S}$. Some phenomenological facts
crucial to its validity are pointed out on the light-through-heavy quarkonium
system.
