Gauge Theories of Vector Particles

Abstract

The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as super-positions of certain “simple” theories; we show that each “simple” theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras—those which admit precisely two commuting quantum numbers—are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called “schizon” model cannot be made to conform to the requirements of partial gauge-invariance. It is possible, however, to find a formal theory of four intermediate bosons that is partially gauge-invariant and gives an approximate │ΔI│= 1/2 rule.