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We consider the $pipi$-scattering problem in the context of the Kadyshevsky equation. In this scheme, we introduce a momentum grid and provide an isospectral definition of the phase-shift based on the spectral shift of a Chebyshev angle. We address the problem of the unnatural high momentum tails present in the fitted interactions which reaches energies far beyond the maximal center-of-mass energy of $sqrt{s}=1.4$ GeV. It turns out that these tails can be integrated out by using a block-diagonal generator of the SRG.
The solution of the scattering problem based on the Lippmann-Schwinger equation requires in many cases a discretization of the spectrum in the continuum which does not respect the unitary equivalence of the S-matrix on the finite grid. We present a n
The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among unitarily equiv
Dense relativistic matter has attracted a lot of attention over many decades now, with a focus on an understanding of the phase structure and thermodynamics of dense strong-interaction matter. The analysis of dense strong-interaction matter is compli
A Wilsonian approach based on the Similarity Renormalization Group to $pipi$ scattering is analyzed in the $JI=$00, 11 and 02 channels in momentum space up to a maximal CM energy of $sqrt{s}=1.4$ GeV. We identify the Hamiltonian by means of the 3D re
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a chall