# Quantum Extended Crystal Super Pde&#x27;s - Mathematics > Algebraic Topology

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Abstract: We generalize our geometric theory on extended crystal PDE-s and theirstability, to the category $\mathfrak{Q} S$ of quantum supermanifolds. By usingalgebraic topologic techniques, obstructions to the existence of global quantumsmooth solutions for such equations are obtained. Applications are given toencode quantum dynamics of nuclear nuclides, identified withgraviton-quark-gluon plasmas, and study their stability. We prove that suchquantum dynamical systems are encoded by suitable quantum extended crystalYang-Mills super PDE-s. In this way stable nuclear-charged plasmas and nuclidesare characterized as suitable stable quantum solutions of such quantumYang-Mills super PDE-s. An existence theorem of local and global solutions withmass-gap, is given for quantum super Yang-Mills PDE-s, $\hat{YM}$, byidentifying a suitable constraint, $\hat{Higgs}\subset \hat{YM}$, {\emHiggs quantum super PDE}, bounded by a quantum super partial differentialrelation $\hat{Goldstone}\subset \hat{YM}$, {\em quantumGoldstone-boundary}. A global solution $V\subset\hat{YM}$, crossing thequantum Goldstone-boundary acquires or loses mass. Stability properties ofsuch solutions are characterized.

Autor: Agostino Prastaro

Fuente: https://arxiv.org/