Infinite-momentum Limit Research Articles

Superconvergence Relations for Mesons and Higher Symmetries

Superconvergence relations for meson-meson scattering are obtained on the basis of locality and unitarity, and they are selected using the infinite-momentum limit. Complete saturation of these superconvergence relations with nonets of pseudoscalar and vector mesons gives rise to a consistent set of relations between coupling constants. These equations have a unique solution which is consistent with collinear $U(6)$ symmetry for the vertices. It is proposed that this result remains unchanged if additional intermediate states are introduced in sets corresponding to higher representations of $U(6)\ensuremath{\bigotimes}U(6)\ensuremath{\bigotimes}O(3)$ which separately satisfy the relations.

Relations for theN−N*Weak Form Factors from Current Algebra in the Infinite-Momentum Limit

The nucleon matrix elements of an $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{SU}(2)$ subalgebra of ${U}_{6}\ensuremath{\bigotimes}{U}_{6}$ are considered in the infinite-momentum, nonzero-momentum-transfer limit. Only the $N$ and ${N}^{*}$ intermediate states are retained. In this approximation we reproduce the results of the dispersive approach while also obtaining Oehme's equation which was derived for the zero-momentum-transfer case.

Current Algebras at Infinite Momentum

We examine the mathematical properties of the "infinite-momentum limit" of current-density operators. Free-field currents are examined for heuristic purposes. For physical particles we consider the restrictions of the current-density operators to the one-particle subspace. The existence of an operator limit is demonstrated for scalars, vectors, and antisymmetric tensors. The limit vanishes for scalars and, except in special cases, diverges for higher tensors. The kernels of the limit operators are obtained explicitly as functions of the same invariant form factors that determine the kernels of the original current densities. Commutation relations for the integrated currents are dynamical hypotheses. "Local" commutation relations for the densities at infinite momentum are incompatible with the assumption that the spins are bounded in the one-particle subspace.

Superconvergent Dispersion Relations and Vector-Meson-Baryon Couplings

Matrix elements of the equal-time commutators of an octet of vector current densities are considered in the infinite-momentum limit. As a consequence of locality, the Fourier transforms of these matrix elements are polynomials in the components of the momentum transfer. The resulting superconvergent sum rules are saturated with the octet and the decimet of baryons, and are evaluated at the double pole due to vector mesons. A consistent set of approximate equations for vector-meson-baryon couplings is obtained. This set has a unique nontrivial solution for the coupling constants. Together with a meson pole model for the electromagnetic form factors of baryons, these couplings give rise to relations for the form factors which are in good agreement with experiments. They are also consistent with the results obtained on the basis of collinear $U(6)$ symmetry.

SU(6)WAlgebra and the Commutators of Electric Dipoles at Infinite Momentum

The saturation of the ${\mathrm{SU}(6)}_{W}$ algebra at infinite momentum is discussed. A possible physical interpretation of the tensor generators of ${\mathrm{SU}(6)}_{W}$ in terms of an assumption of partial conservation is critically analyzed. The implied occurrence of singularities in the tensor amplitudes requires a careful definition of a limiting procedure defining the tensor charges. A collinear limiting procedure, which relates the tensor charges to the total magnetic moments, appears as the most convenient one. The matrix elements of the tensor charges are then compared in the infinite-momentum limit with those of the electric dipoles, and the following implications are exhibited: The charge radii of baryons are pure $F$; the $\frac{D}{F}$ ratio of axial charges equals the corresponding ratio for the total baryon magnetic moments; a simple relation exists among the isovector total moment of the nucleon, the axial renormalization constant, and the charge radius of the proton; and an extended form of universality holds for tensor and axial currents. We also discuss the saturation of the unitary symmetric part of the commutators, particularly in connection with the possible occurrence of Schwinger terms.