Fermion propagator diagonalization and eigenvalue problem
D.A. Dolzhikov (1), A.E. Kaloshin (1, 2), V.P. Lomov (2, 3), ((1) Joint Institute for Nuclear Research, (2) Irkutsk State University, (3), Institute for System Dynamics, Control Theory)
TL;DR
This paper presents a method for diagonalizing fermion propagators using an eigenvalue problem approach, providing a simple algebraic transformation useful for on-shell fermions and fermion mixing matrix renormalization.
Contribution
It introduces a novel similarity transformation technique for fermion propagator diagonalization based on eigenvalue problems, simplifying algebraic properties for on-shell fermions.
Findings
Derived a similarity transformation for propagator diagonalization
Simplified algebraic properties for on-shell fermions
Applicable to renormalization of fermion mixing matrices
Abstract
We discuss diagonalization of propagator for mixing fermions system based on the eigenvalue problem. The similarity transformation converting matrix propagator into diagonal form is obtained. The suggested diagonalization has simple algebraic properties for on-shell fermions and can be used in renormalization of fermion mixing matrix.
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