By A. W. Thomas (auth.), J. W. Negele, Erich Vogt (eds.)
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Extra info for Advances in Nuclear Physics: Volume 13
53). Actually a much more appropriate term would be hidden chiral symmetry because Eq. 54) is invariant under the chiral transformation a-+a-g'!! -+ !! 58) Finally, the conserved vector current associated with Eq. 3. PCAC in the a-Model Having obtained a chiral-symmetric theory with a nucleon mass, all we need to do to make contact with the real world is to introduce a mass for the pion. 62) Chiral Symmetry and the Bag Model 51 in Eq. 65) Because we broke the chiral SU(2) symmetry with the -ca term, the axial current is no longer conserved.
However, at some critical field strength there is a phase transition to a highly complicated vaClum state with color-dielectric constant ~ -* 0, thus confining color fields. In the Princeton picture the pion appears as an ess,ential part of this process (Cal+ 78, Cal+ 79). As we shall discuss further in Sections 4 and 5, in their picture, it is a Goldstone boson associated with the breaking of chiral symmetry in the complicated vacuum outside the bag. It contributes to the bag pressure. Goldman and Haymaker (GH 81, HG 81) have recently demonstated how pion and sigma (scalar-isoscalar) fields can appear as a result of dynamical symmetry breaking in a model of the Jona-Lasinio-Nambu type (NJ 61).
6 * However, suppose that there is a non zero quark density at same point in space, which we can choose to be r = O. ) The second term on the right-hand side of Eq. 105) is then linear in 0: as shown in Fig. 4. Clearly, if either g or qq is large enough, it is possible that the minimum energy will occur at a = 0 rather than a = a v ' In this region the quark and sigma fields obey coupled linear equations (Ci . 108) k where a o is the time-independent, mean a-field. Same typical solutions of these equations are plotted in Fig.