# Locally Gauge-Invariant Formulation of Parastatistics

## Abstract

The color degree of freedom of hadronic physics was first Introduced [4] in the context of para-Fermi statistics of order three for quarks. Bose and Fermi combinations of para-Fermi quarks are in one-to-one correspondence with the color singlets of the formulation with explicit color [11]. Thus the counting of states, and the explanation of the apparent conflict with the spin-statistics theorem with quarks in the symmetric representation of SU(6) [9] are In agreement with the explicit color formulation, as is the “symmetric quark model” for baryons[4,6], which was first proposed In the context of the para-Fermi formulation. Other predictions of the two formulations which agree Include the decay rate for π ^{0} to two photons, and, at least from the standpoint of naive counting, the ratio of the cross sections of e^{+}e^{−} to hadrons to that to μ^{+}μ^{−}. The gauge theory of color, quantum chromodynamics (QCD) differs, however, from the ungauged parastatistics formulation in predictions involving gluons, such as quark and gluon Jets and the existence of glueballs. The main point of this talk is that parastatistics can be gauged and that, when gauged, it is equivalent to the corresponding Yang-Mills gauge theory, in particular, for the case of para-Fermi quarks of order three, to QCD [81].

## Keywords

Gauge Theory Clifford Algebra Spinor Field Anticommutation Relation Color Degree## Preview

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