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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.
We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost and the ge
We study the eigenvalue equation for the Cartesian coordinates observables $x_i$ on the fully $O(2)$-covariant fuzzy circle ${S^1_Lambda}_{Lambdainmathbb{N}}$ ($i=1,2$) and on the fully $O(3)$-covariant fuzzy 2-sphere ${S^2_Lambda}_{Lambdainmathbb{N}
Starting from Wigners symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl sp
We discuss the (right) eigenvalue equation for $mathbb{H}$, $mathbb{C}$ and $mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic
We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tr