Spectral Breakdown Theory

We present the theory of spectral breakdown via renormalization and decoherence. In our concept, renormalization reduces the multiplicity of a function by dividing it by its or its multiple roots (multiplicity -1) and decoherence removes the imaginary parts of complex roots by projecting them onto the real axis which reduces the complexity of the function.Here the spectral break is a transformation of a complex function P into a simple function q and the spectral distance measures the proximity between the roots of P and q (the spectral distance between the roots of P and q), the spectral distance is in a spectral plane and not Euclidean so the spectral distance can be complex. In our article we introduce a new concept of minimal rupture, it is the minimum of P and q. Spectral breakdown is a nonlinear and irreversible transformation because of the decoherence which removes the majority of the identity of the function and the renormalization which reduces the multiplicity of function. NB: Renormalization is applied before decoherence.