Scattering Amplitudes
doi: 10.2172/5234309
Su Groups
ark: ark:/67531/metadc1070576
1/N
Symmetry Groups 645400* -- High Energy Physics-- Field Theory
72 Physics Of Elementary Particles And Fields
Series Expansion
Quantum Chromodynamics
Stanford Linear Accelerator Center
Field Theories
So Groups
There exist families of field theories with symmetry group SO(N) (or SU(N)) that become simpler as N becomes larger. More precisely, the solutions to these theories possess an expansion in powers of 1/N. This expansion is the subject of these lectures. The 1/N expansion can be used to analyze model field theories. The 1/N expansion is developed for phi/sup 4/ theory and applied to two two-dimensional models with similar combinatoric structures, the Gross-Neveu model and the CP/sup N-1/ model. These models display (in the leading 1/N approximation) such interesting phenomena as asymptotic freedom, dynamical symmetry breaking, dimensional transmutation, and non-perturbative confinement. It is possible that the 1/N expansion, with N the number of colors, might fruitfully be applied to quantum chromodynamics. Unfortunately, it is not possible to make a decisive test of the approximation, because no one knows how to compute even the first term in the expansion in closed form. However, it is possible to argue that this first term, whatever its detailed form, has many properties that are also shared by the real world, and which are otherwise underived from field theory. These include the saturation of scattering amplitudes by an infinite number of narrow resonances, the essential feature of dual-resonance models. (RWR)
grantno: AC03-76SF00515
Symmetry Breaking
1980-03-01
Quantum Field Theory
Phi4-Field Theory
osti: 5234309
Amplitudes
Lie Groups
Pages: 72
Coleman, S.
rep-no: SLAC-PUB-2484