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Infinite-Momentum Limit of a Spinor Field Theory
David Flory (Yeshiva University)
Abstract: Weinberg has shown that in an infinite-momentum frame moving along the $\ensuremath{-}z$ axis, the old-fashioned perturbation-theory graphs containing intermediate particles with negative ${p}_{z}$ vanish. This result is here extended to a theory of spin-\textonehalf{} and scalar or pseudoscalar particles with a $g\overline{\ensuremath{\psi}}\ensuremath{\Gamma}\ensuremath{\psi}\ensuremath{\phi}$ interaction ($\ensuremath{\Gamma}=1 or {\ensuremath{\gamma}}^{5}$) in a tree-graph approximation. The effect of the particles with negative ${p}_{z}$ is absorbed into a counterterm in the Hamiltonian. This counterterm is of order ${g}^{2}$ in the coupling constant.