A Particle Model That Produces Feynman Diagrams: Re-examination of Fundamental Entities, Free Particles, and Background Frames

Abstract

A relativistic quantized particle model avoids difficulties through (1) a Hamiltonian undecomposable into H=H(0)+H(I), (2) a separation of the evolution parameter s from dynamics, (3) "leptons" and "hadrons" composed of "quarks," and (4) the absence of background reference frames. The stringlike Lagrangian is L=-{-[F(Q)]2 [dQ/ds]2+[FdQ/ds]2}1/2. Q(s) defines quark positions; the form of F(Q) determines the interaction. The "strong" Lagrangian is symmetric under quark exchange. Transformation to new quark coordinates "hides" the symmetry. A variational principle for the parametrically invariant action in terms of these coordinates supplies natural boundary conditions (n.b.c.). The resulting symmetry breaking yields "lepton" and "hadron" quarks that behave differently. However, both become "strings" asymptotically. The n.b.c. produce composite mass-shell constraints and suppress time-oscillations. "Strong" scattering between composites is calculated. The "leptons" behave as free particles. A second choice of F(Q) produces unified "electroweak" interactions. First-order perturbation theory is applied to "lepton-lepton" scattering. Unperturbed states are asymptotic solutions from separate "strong interaction" clusters. Transforms between position and momentum representations, determined by the n.b.c., eliminate advanced potentials. Scattering amplitudes obey Feynman rules.