Quantum Extended Crystal Super Pde's

TL;DR

This paper extends geometric theory to quantum supermanifolds, analyzing the stability and existence of solutions for quantum super PDEs, with applications to nuclear physics and quantum dynamics.

Contribution

It introduces a generalized framework for quantum super PDEs, proving existence and stability results, and applies these to model quantum nuclear systems and their mass properties.

Findings

Existence of local and global solutions with mass-gap in quantum super Yang-Mills PDEs.

Quantum solutions crossing the Goldstone-boundary can acquire or lose mass.

Stability properties of quantum solutions are characterized.

Abstract

We generalize our geometric theory on extended crystal PDE's and their stability, to the category $\mathfrak{Q}_S$ of quantum supermanifolds. By using 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 study their stability. We prove that such quantum dynamical systems are encoded by suitable quantum extended crystal Yang-Mills super PDE's. In this way stable nuclear-charged plasmas and nuclides are characterized as suitable stable quantum solutions of such quantum Yang-Mills super PDE's. An existence theorem of local and global solutions with mass-gap, is given for quantum super Yang-Mills PDE's, $\hat{(YM)}$, by identifying a suitable constraint, $\hat{(Higgs)}\subset \hat{(YM)}$, {\em Higgs quantum super PDE}, bounded by a quantum super partial differential relation $\hat{(Goldstone)}\subset \hat{(YM)}$, {\em quantum Goldstone-boundary}. A global solution $V\subset\hat{(YM)}$, crossing the quantum Goldstone-boundary acquires (or loses) mass. Stability properties of such solutions are characterized.