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arXiv · 1501.06337

Mixing of fermions and spectral representation of propagator

A. E. Kaloshin·V. P. Lomov
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Abstract

We develop the spectral representation of propagator for $n$ mixing fermion fields in the case of $\mathsf{P}$-parity violation. The approach based on the eigenvalue problem for inverse matrix propagator makes possible to build the system of orthogonal projectors and to represent the matrix propagator as a sum of poles with positive and negative energies. The procedure of multiplicative renormalization in terms of spectral representation is investigated and the renormalization matrices are obtained in a closed form without the use of perturbation theory. Since in theory with $\mathsf{P}$-parity violation the standard spin projectors do not commute with the dressed propagator, they should be modified. The developed approach allows us to build the modified (dressed) spin projectors for a single fermion and for a system of fermions.

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A. E. Kaloshin, V. P. Lomov. 2015-01-26. Mixing of fermions and spectral representation of propagator. https://doi.org/10.1142/s0217751x16500317

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