Quantum extended crystal super PDEs

We generalize our geometric theory on extended crystal PDEs and their stability, to the category QSQS of quantum supermanifolds. By using the algebraic topologic techniques, obstructions to the existence of global quantum smooth solutions for such equations are obtained. Applications are given to encode quantum dynamics of nuclear nuclides, identified with graviton–quark–gluon plasmas, and to study their stability. We prove that such quantum dynamical systems are encoded by suitable quantum extended crystal Yang–Mills super PDEs. In this way stable nuclear-charged plasmas and nuclides are characterized as suitable stable quantum solutions of such quantum Yang–Mills super PDEs. An existence theorem of local and global solutions with mass-gap, is given for quantum super Yang–Mills PDEs, (YM)̂, by identifying a suitable constraint, (Higgs)̂⊂(YM)̂, Higgs quantum super PDE  , bounded by a quantum super partial differential relation (Goldstone)̂⊂(YM)̂, quantum Goldstone-boundary  . A global solution V⊂(YM)̂, crossing the quantum Goldstone-boundary acquires (or loses) mass. Stability properties of such solutions are characterized.