Pauli Center Blackboard Seminar

On-shell renormalization in the presence of mixing and instability

by Bernd Kniehl (UHH)

Thursday, January 19, 2017 from to (Europe/Berlin)
at DESY Hamburg ( Sem. room 2 )
Description
We consider a system of unstable spin-1/2 fermions in a general
parity-nonconserving theory with intergeneration mixing and explain how to
renormalize its propagator matrix to all orders in perturbation theory. We 
work in the pole scheme, in which the squares of the renormalized masses 
are identified with the complex pole positions and the wave-function 
renormalization (WFR) matrices are adjusted according to the
Lehmann-Symanzik-Zimmermann reduction formalism. Closed analytic 
expressions for the pole-mass counterterms and WFR matrices in terms of 
the self-energy functions are derived. In the Dirac case, we identify 
residual degrees of freedom in the WFR matrices and propose an additional 
renormalization condition to exploit them. By contrast, the WFR matrices 
are uniquely fixed in the Majorana case. We demonstrate that, in the 
presence of instability, the WFR matrices of the in and out states 
bifurcate in the sense that they are no longer related by pseudo-Hermitian 
conjugation.