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Breaking of chiral symmetry

Chiral symmetry implies that the fermions of the theory should be massless. However this restriction can be eliminated by the construction of a theory in which the fermion mass arises as part of the interaction. One way to do this, is to construct a theory in which the fermions start off as massless and to generate their masses through the mechanism of spontaneous symmetry breaking, but we have to accept the presence of massless pseudoscalar particles.

At zero temperature the ``potential energy'' of such a theory exhibits only one minimum which corresponds to the lowest energy state of the system (in field theory it corresponds to the vacuum). This theory can be used to describe massless fermions interacting with massive mesons. In the case of two mesons the potential is given in figure 1.

Figure 1: The ``potential'' before symmetry breaking
Due to the appearance of a constant classical field which covers the whole space, this potential acquires extra minima and we say then that the symmetry is broken or hidden. The theory now can describe massive fermions which acquired their masses through the scalar field. There are also massive scalar particles but there some mystery now because massless particles appear as well, which are called the Goldstone bosons. For two meson fields we can picture this situation with the famous ``Mexican hat potential'' or `` wine bottle bottom'' of figure 2.
Figure 2: The ``potential'' after symmetry breaking


next up previous
Next: The chiral phase transition Up: No Title Previous: Chiral Symmetry
Nicholas Petropoulos
3/13/1998