Abstract
The main aspects of chiral symmetry in QCD are presented. The necessity of its spontaneous breakdown is explained. Some low-energy theorems are reviewed. The role of chiral effective Lagrangians in the formulation and realization of chiral perturbation theory is emphasized. The consequences of the presence of anomalies are sketched.
Highlights
Symmetries play an important role in quantum field theory. (For general surveys, one may consult, e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12].) They introduce limitations in the choice of possible interactions for a given physical problem or phenomenon and often they completely fix the structure of the Lagrangian of the theory
The situation would be different had we introduced the symmetry breaking through the coupling constants of the interaction terms, by assigning a different coupling constant to each flavor type quark
The symmetry breaking could be treated as a perturbation only if the quark masses are much smaller than the QCD mass scale
Summary
Symmetries play an important role in quantum field theory. (For general surveys, one may consult, e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12].) They introduce limitations in the choice of possible interactions for a given physical problem or phenomenon and often they completely fix the structure of the Lagrangian of the theory. One distinguishes two types of symmetry, local ones, where the parameters of the transformations are spacetime dependent, and global ones, where the latter are spacetime independent. Local symmetries lead in general to the introduction of gauge theories, while global symmetries classify particles according to quantum numbers or predict the existence of massless particles. QCD, the theory of strong interaction, is a gauge theory with the local symmetry group S U(Nc), acting in the internal space of color degrees of freedom. The fundamental fields are the quarks (matter fields) and the gluons (gauge fields). With a common mass parameter m, belong to the defining fundamental representation of the color group, which is Nc-dimensional, antiquark fields to the complex conjugate representation of the latter (Nc-dimensional), while the gluon fields, which are massless, belong to the adjoint representation ((Nc2 − 1)-dimensional)
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