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We study a new form of dynamical system, in which the commutation relations for the dynamical variables of a quantized field are defined on a "lightlike surface" 7 = (t + z)/ d/z = 0 rather than at one instant of time t = 0. We clarify the physical implications of the use of the new variables x1 = x, x2 = y, x+ = (t + z)/2/Z, x-= (t -z)/v'/z and explore its significance as a new form of relativistic dynamics, which holds in any Lorentz frame but not in the so-called "infinite momentum frame." Using the quark model, we build up a new algebra of currents, in which the current commutators are detined at equal +. The sum rules and other results of the usual current algebra can be obtained without taking the unjustifiable limit of infinite momentum. In particular, we obtain the Gell-Mann-Okubo mass formulas in quadratic form for both mesons and baryons without the trouble due to momentum dependence. We derive the reduction formula and find the physical high energy limit (not the Bjorken limit) of an amplitude is determined by the equal 7 commutator.
📜 SIMILAR VOLUMES
We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering and two ph