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By V. N. Gribov
This paintings presents a different advent to the speculation of advanced angular momenta, in accordance with the equipment of box thought. It contains an English translation of a lecture direction given by way of Vladimir Gribov in 1969. along with their ancient value, those lectures comprise fabric hugely proper to investigate this day and sure to shape the foundation for destiny advancements within the topic.
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Extra resources for The Theory of Complex Angular Momenta: Gribov Lectures on Theoretical Physics
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5a) Analogously, s1(2) is the squared 4-momentum transfer between the intermediate and the initial (final) state; z1 , z2 are the cosines of the corresponding scattering angles: s1 = −2kt2 (1 − z1 ), s2 = −2kt2 (1 − z2 ). 5b) It is convenient to replace integration over the azimuthal angle φ in dΩ = dz1 dφ by that over z2 using the trigonometric relation z2 = zz1 + (1 − z12 )(1 − z 2 ) cos φ . 7a) where K ≡ (z − z1 z2 )2 − (1 − z12 )(1 − z22 ). 8) with the integration domain determined by the condition K(z, z1 , z2 ) < 0.
19) f | =n = fn . 20) where the integration contour L is shown in Fig. 3. ) ♠ ✻ L ✲ ✤ • 0 • ✣ Fig. 3. 20), P (z) is the Legendre function of the first kind, the solution of the differential Legendre equation that is regular at z = 1. Let us now † We use here the letter n instead of to emphasize that the partial waves in this sum are defined only for integer values of the angular momentum. 32 2 Physics of the t-channel and complex angular momenta deform the contour along the imaginary axis. 20) should decrease at large | | in the right half-plane.
L ✲ ✤ • 0 • ✣ Fig. 3. 20), P (z) is the Legendre function of the first kind, the solution of the differential Legendre equation that is regular at z = 1. Let us now † We use here the letter n instead of to emphasize that the partial waves in this sum are defined only for integer values of the angular momentum. 32 2 Physics of the t-channel and complex angular momenta deform the contour along the imaginary axis. 20) should decrease at large | | in the right half-plane. 21b) where z = cos Θ. 21) we conclude that the ratio P (−z)/ sin π falls exponentially with Im → ∞ in the physical region 0 < Θ < π.