Multiperipheral Dynamics at Zero Momentum Transfer

Abstract

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Broken Chiral Symmetry. III.SW(3)Theory and Soft-Pion Corrections

“…Together with the ordinary isospin group SU(2), the point a = -1 then corresponds to the validity of the SIV(2) =SU(+)(2)@SU(-) (2) subgroup. Note that we nolonger have an additional conservation law a,A,(-l)(x) = O as in the bV(3) case, so that our subgroup a t a = -1 is SIV(2) rather than FV (2). In particular, we do not have to worry about the question whether 7 and X mesons would become soft a t a = -1.…”

“…I n order to realize the special subgroups with degenerate vacua, one can show from general considerations of the two-point functions and positive definiteness of Hilbert space, that the end points must be essentially singular. Now regarding the physical quantities or nlatrix elements as continuous functions of the symmetry-breaking parameter under consideration in the physical domain, and using general principles such as current algebra, soft-meson methods, and variational techniques, we can impose considerable restrictions on the functional dependence, which leads to several interesting results, some of which have been derived in I. I n this way, one can, for instance, fix the "physical" value of the symmetry-breaking parameters, and one finds, in agreement with the worli of Gell-Mann, Oalies, and R e n n e~,~.~ that whereas the Hamiltonian is approxin~ately invariant under the TV (2) symmetry, the vacuum state is predominantly an SU(3) singlet.…”

“…At the point under consideration on the hyperbola, what symmetry group does one realize, and is this larger than the syininetry [presumably SU (2)] of the vacuum? Also, would this point be an essentially singular point of the theory?…”