By Professor Dr. Walter Greiner, Professor Dr. Andreas Schäfer (auth.)
ISBN-10: 3540780505
ISBN-13: 9783540780502
ISBN-10: 3642579787
ISBN-13: 9783642579783
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Extra resources for Quantum Chromodynamics
Example text
And thus must have spin 1, there are only two independent spin projections and not three, as one might naively expect. As we have seen, this result is rooted in the photons having no mass. 116), the theory would no longer be gauge invariant and gauge freedom would be lost. We thus describe incoming photons with four-momentum p and polarization state >. by the wave function >. 139) >. 140) and outgoing photons by AJ1. ) . 141) holds. 142) as the normalization factor. 118, 119) for particles with a mass.
The difference between the direct parts of the amplitudes for 7r+7r- scattering (or 7r+K+ scattering) and 7r+7r+ scattering is only that of sign if the corresponding four-momenta are considered equal (because of the different masses of K+ and 7r- they are in general not equal). The different signs of these two processes correspond to attractive and repulsive interaction, respectively. 6 The Cross Section for Pion-Kaon Scattering Problem. Derive the explicit form of the differential cross section for electromagnetic 7r+K+ scattering in the center-of-momentum system (ems).
2. Review of Relativistic Field Theory 2PI . P2 = 2P3 . P4 = 2PI . P4 = mt + m~ - S - u m~ - m~ . (30) With the help of these relations the invariant scattering amplitude (2) assumes the form (31) where we have transformed the fine-structure constant e2 1 (32) a = 411" :::= 137 to so-called Heaviside-Lorentz units. In these units Gauss's law reads yo . E = p. It is particularly simple to transform (31) into the cm system, since we have, according to (29) and (5), ,oi = E;ms s = (E\ +E2 u = (E\ -E4,P + p'i = (E\ -E4i - (p + p'i = = Ef + E1- 2EIE4 - (Ef - m~) - (E1- m~) - 2p· p' 2E\E4 .
Quantum Chromodynamics by Professor Dr. Walter Greiner, Professor Dr. Andreas Schäfer (auth.)
by Kenneth
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