Abstract
Renormalization group procedure for effective particles (RGPEP) is applied to a theory of fermions that interact only through mass mixing terms in their Hamiltonian. Problems with virtual pair production in vacuum are avoided by using the front form of Hamiltonian dynamics. Masses and states of physical fermions emerge at the end of a calculation that is carried out exactly irrespective of the strength of the mass mixing terms. An a priori infinite set of renormalization group equations for all momentum modes of fermion quantum fields is reduced to just one equation for a two-by-two mass matrix. In distinction from scalars, fermions never become tachyons but appear chirally rotated when the mass mixing interaction term is sufficiently strong.
Highlights
Among the issues that need to be dealt with on the way to defining and solving relativistic quantum field theory beyond the perturbative pictures based on free propagation or weak binding of field quanta, one may distinguish the issues of vacuum and renormalization, both intricately related with the struggle to understand relativity and quantum mechanics simultaneously in one theory
This article offers a description of how the renormalization group procedure for effective particles (RGPEP) can be applied to an elementary quantum field theory for the relativistic fermions that interact through a mass mixing term of arbitrary strength [1]
The vacuum issue is addressed by using the front form (FF) of dynamics instead of the familiar instant form (IF) [2]
Summary
Among the issues that need to be dealt with on the way to defining and solving relativistic quantum field theory beyond the perturbative pictures based on free propagation or weak binding of field quanta, one may distinguish the issues of vacuum and renormalization, both intricately related with the struggle to understand relativity and quantum mechanics simultaneously in one theory. Literature concerning these two issues is of enormous size and scope and this article is not to review it. The RGPEP approach is presented in a concise form that indicates new elements in comparison with the IF approach
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