TL;DR
This paper introduces a gauge-invariant mass function in gauge theories, providing a consistent off-shell mass definition that parallels the on-shell pole mass, through renormalization.
Contribution
It demonstrates that renormalization yields a gauge-invariant mass function at all virtualities, clarifying the off-shell mass concept in gauge theories.
Findings
Renormalization defines a gauge-invariant mass function at every virtuality.
The off-shell propagator's mass can be made gauge-invariant, similar to the on-shell pole mass.
The distinction between on-shell and off-shell mass is purely kinematic, not dynamical.
Abstract
In gauge theories, the mass of a field has been regarded as a purely on-shell concept: the pole mass is gauge-invariant, but the off-shell propagator has had no gauge-invariant definition of mass. We show that renormalization defines a gauge-invariant mass function at every virtuality, together with a gauge-invariant vertex. The virtual particle becomes as well defined as the on-shell one: the distinction is not dynamical but purely kinematic.
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