By John M. Howie
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Extra resources for An Introduction to Semigroup Theory (L.M.S. Monographs ; 7)
We will, therefore, have to know how the vacuum state responds to symmetry transformations. Let U (ε) denote the unitary representations of the symmetry group in the Fock space of a given ﬁeld theory. 1) L(φ , ∂µ φ ) = L(φ, ∂µ φ). 2) and The vacuum state |0 may or may not be invariant under U(ε). Let us consider both these cases. Case (i): U(ε)|0 = |0 . This is known as the Wigner–Weyl mode of symmetry realization. We can show that, in this case, there exists mass degeneracy between particles in a supermultiplet as well as relations between coupling constants and scattering amplitudes.
An immediate problem was to understand why long-range forces resulting from single gluon exchange have not been seen. Similarly, since gluons are massless, they should be copiously produced in all strong interaction β=− 14 1. Important Basic Concepts in Particle Physics processes. Furthermore, since at high energies quarks become free, they should have been seen because their masses are expected to be less than the nucleon mass. To resolve this conundrum, a new principle, known as “conﬁnement,” was introduced .
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An Introduction to Semigroup Theory (L.M.S. Monographs ; 7) by John M. Howie