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6. 7 depends on the presence of a quadratic term in the unitarity relation. Therefore, the Froissart bound holds only for purely-hadronic processes. In particular, it imposes no constraint on either real or virtual Compton scattering. 4, where we draw attention to the lack of a Froissart-bound constraint on the small-x behaviour of the proton structure function F2 (x, Q2 ). During the late 1960s there was a great deal of research on the algebra of currents, in particular of the weak current. 62) does the electromagnetic current, and using the canonical equal-time anticommutation relations for these fields, one may deduce equal-time commutation relations for the currents and various useful consequences follow[38].
15) become ± βi± (t)Γ(−αi± (t)) (1 ± e−iπαi A± (s, t) ∼ (t) ± ) (s/s0 )αi (t) . 17) is the Regge representation for A± (s, t): it gives the behaviour of A± (s, t) for large s and small t. √ The background integrals must be added. Their integrands vanish as 1/ s for large s. We shall describe in appendix A how Mandelstam manipulated the background integrals so that when he pushed them further to the left in the l-plane he could make them arbitrarily small. 15), together with the contributions from branch points and their attached cuts.
Total cross sections continued for some fixed and unknown value of s0 . This bound applies in the limit s → ∞, but it is often assumed that in practice currently-accessible energies are high enough. However, at present-day energies the bound is more than 100 times greater than measured values, taking s0 in the range 1 to 10 GeV2 , so it is not really a significant constraint. 4) where P is the momentum of the particle a in the rest frame of particle b (so √ that at high centre-of-mass energy s it is proportional to s).