Gauge invariance in quantum hadrodynamics

This paper describes the derivation of a new representation of an $SU(2)_L \times SU(2)_R$ locally-invariant model of the strong interactions called quantum hadrodynamics 3 (QHD-III). QHD-III is a gauge-invariant theory based on the linear $\sigma$ model, the gauge bosons being the $\rho$ and the $a_1$. The new representation considerably simplifies the lagrangian. To derive the new representation, the gauge invariance of the model is exploited. The role of the gauge boson masses in gauge-invariant models of the strong interactions based on the $\sigma$ model is also discussed, and it is shown that these masses are necessary if the pion is to survive as a physical field.