The effect of the choice of wave functions on theoretical predictions for symmetry breaking processes: A view from the DKP formalism

When considering an elementary particle matrix element, of necessity one must make an assumption, which often goes unnoticed, as tho what formalism should be used for the wave functions. A current or interaction Lagrangian-density matrix-element is of the form V = anti PSIsub(out)GAMMA PSIsub(in), where PSIsub(in) and anti PSIsub(out) represent the physical ingoing and outgoing particles, and GAMMA represents the vertex function. A current must have the dimensions of (length)-3 = (mass)3 in units of h/2π = c = 1. PSIsub(in) and anti PSIsub(out) must be described in terms of the physical on-shell masses or else one has no phase space. It is only the vertex function which can be symmetric in the internal symmetry under consideration. The decision as to how much of the matrix element will be taken to be symmetric and how much of the matrix element will be taken to be associated with on-mass-shell wave functions is a fundamental assumption. Depending on how the assumption is made, different results will be predicted. Normally first-order Dirac wave functions, with dimensions (length)sup(-3/2) and second-order Klein-Gorddon wave functions with dimensions (length)-1 are considered for spin-1/2 fermions and spin-O bosons, respectively. We will discuss the types of new results which are obtained if, on the contrary, one chooses to consider bosons in the first-order Duffin-Kemmer-Petiau formalism. We will argue that the DKP formalism represents a complementary viewpoint to the spectrum generating approach. Both challenge the standard phenomenology: DKP by changing the wave function, spectrum generating by changing the vertex function. (orig.)