Theories with Gauge Groups
The success of quantum electrodynamics suggests the investigation of theories constructed in analogy with it. The gauge invariance of second kind with variable phase functions can be viewed as a generalization of the gauge invariance of first kind (with constant phase) which forces the introduction of the electromagnetic potential, so that the gauge transformation on the matter field can be cancelled by the gauge transformation of the potential. In this way, the generalization of the gauge transformation to a coordinate dependent transformation can be taken as the principle generating the electromagnetic field. This point of view has been applied (Yang-Mills ) to the group of isospin transformations of a nucleon field. When these transformations are made coordinate dependent, one is led to introduce a vector field, the b field, which is both a Lorentz vector and an isospin vector, and which is the analogue of the electromagnetic potential. The theory of Yang and Mills is described in Section 3 after a brief review of electrodynamics, given in Section 2.
KeywordsGauge Group Field Equation Gauge Transformation Vector Meson Gauge Invariance
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