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Quantum extended crystal super PDEs. (English) Zbl 1258.81064

Summary: We generalize our geometric theory on extended crystal PDEs and their stability, to the category \(\mathfrak Q_{S}\) 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, \(\widehat {(\text{YM})}\), by identifying a suitable constraint, \(\widehat {(\text{Higgs})}\subset \widehat {(\text{YM})}\), Higgs quantum super PDE, bounded by a quantum super partial differential relation \(\widehat {(\text{Goldstone})}\subset \widehat {(\text{YM})}\), quantum Goldstone-boundary. A global solution \(V\subset \widehat {(\text{YM})}\), crossing the quantum Goldstone-boundary acquires (or loses) mass. Stability properties of such solutions are characterized.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
81T60 Supersymmetric field theories in quantum mechanics
35Q40 PDEs in connection with quantum mechanics
81V22 Unified quantum theories
83E50 Supergravity
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