By Vladimir Gribov

This vintage booklet derives from a lecture direction Vladimir Gribov, who was once one of many founding fathers of high-energy straight forward particle physics, dropped at graduate scholars within the 1970's. It therefore presents trendy graduate scholars and researchers with the chance to profit from the instructing of 1 of the twentieth-century's maximum physicists. Its content material continues to be deeply suitable to trendy learn, for instance exploring houses of the relativistic conception of hadron interactions in a website of peripheral collisions and big distances that quantum chromodynamics has slightly approached. It covers a mixture of issues no longer handled somewhere else, whereas final self-contained and obtainable at a graduate point.

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Extra info for Strong Interactions of Hadrons at High Energies: Gribov Lectures on Theoretical Physics (Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)

Example text

3 Higher orders 43 1 3 1 2 4 4 = 3 2 u≥ 4m 2 Fig. 4 The crossed box graph having branch cuts in t and u. Arrows mark the direction of the positive energy flow. t 2 m 2 m =4 u= u t = 4m2 t=0 s Fig. 5 s= 4m 2 s= m2 u Singularities of the second order amplitude on the Mandelstam plane. 2 Scattering amplitude as a function of s Nine cut diagrams contained in Fig. 1 describe the imaginary part of the full two particle scattering amplitude in the order λ4 , due to the schannel threshold. The same diagrams with permuted external particles give t- and u-channel complexities.

1 Causality and analyticity 33 where f0 does not contribute to the scattering: d4 y f0 (y) exp{ip1 y} = 0. 4b) does not imply f0 ≡ 0, since it is only the Fourier components with a physical momentum p1 , p1 = m2 + p2 , p , that are required to vanish. How does such a decomposition emerge in the field theory? 4) is to invoke the general operator language. 5) ¯ 1 ) ∓ ψ(y ¯ 1 )ψ(y3 ) ± ψ(y ¯ 1 )ψ(y3 ), = ϑ(Δy0 ) ψ(y3 )ψ(y where Δy stands for the relative coordinate, Δy μ = y3μ − y1μ . e. particles with integer and half-integer spin.

To make this interpretation valid, we must take the energy components of the momenta p3 and p2 to be negative: p30 ≤ −m3 and p20 ≤ −m2 . But as you know, in the relativistic theory the propagation of a negative energy particle 3 with a momentum p3 corresponds to the propagation of its antiparticle (¯ 3) with the four-momentum p¯3 = −p3 . Therefore, in this region of momenta the very same diagram describes another physical process, namely a collision between the particle 1 and the antiparticle ¯3 (having a four-momentum p¯3 = −p3 ), which results in the production of particles 4 and ¯2 in the final state.

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