A chiralspin symmetry in QCD in Minkowski space-time

In this paper, we look how to construct in Minkowski space-time a new type of \textit{chiralspin} group transformation of the spinor fields, similar to the one discovered by recent works of \textit{Glozman et al.} in the context of high temperature QCD and truncated studies in lattice calculations. Afterwards, we prove the invariance of free massless fermionic action under such group transformations, as well the invariance of the Hamiltonian of free massless fermions. At the end, the possible presence of a symmetry driven by such new \textit{chiralspin} group at high temperature QCD, also at non zero chemical potential, is discussed.