Connection between Gauge Invariance and Mass

The limit, as the bare mass vanishes, of a theory of a massive neutral vector meson interacting with charged fields is investigated. A redefinition of the charged-field operators is exhibited so that the original theory, involving a positive definite metric, goes over smoothly to a radiation gauge theory. The spectral forms for the boson two-point function are exhibited to show that the limit to a gauge-invariant theory does not restrict the interacting mass of the vector particle. A soluble example is given in which these limits can be studied in detail and in which the gauge-invariant limit describes a massive vector particle.