Abstract
In the paper, within the background field method, the structure of renormalizations is studied as for Yang–Mills fields interacting with a multiplet of spinor fields. By extending the Faddeev–Popov action with extra fields and parameters, one is allowed to establish the multiplicative character of the renormalizability. The renormalization of the physical parameters is shown to be gauge-independent.
Highlights
When quantizing non-Abelian gauge field theories [1], whose gauge transformations form a group, one is naturally based on the Faddeev–Popov method [2]
It is a characteristic property of the Faddeev–Popov gauge-fixed action that the latter is invariant under global BRST supersymmetry [3,4], which, in turn, can be expressed in the form of the Zinn-Justin equation [5] for the Faddeev–Popov action
There are many papers devoted to various aspects of renormalizability of Yang–Mills theories, gauge dependence of renormalization constants has been studied explicitly only as for the gauge field sector [20]
Summary
When quantizing non-Abelian gauge field theories [1], whose gauge transformations form a group, one is naturally based on the Faddeev–Popov method [2] It is a characteristic property of the Faddeev–Popov gauge-fixed action that the latter is invariant under global BRST supersymmetry [3,4], which, in turn, can be expressed in the form of the Zinn-Justin equation [5] for the Faddeev–Popov action. There are many papers devoted to various aspects of renormalizability of Yang–Mills theories, gauge dependence of renormalization constants has been studied explicitly only as for the gauge field sector [20]. Within the background field formalism, it is studied a multiplicative renormalization procedure and gauge dependence as for Yang–Mills fields interacting with a multiplet of spinor fields. Right derivatives of a quantity f with respect to the variable φ are denoted as f
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